[1]
a^2+b^2=c^2
ã®é¢ä¿åŒãæºããæŽæ°(a,b,c)ã¯ããç¥ãããŠããçµåãã§ããã
1/a^2+1/b^2=1/c^2
ãæºãã(a,b,c)ãæ¢ããš
1/65^2+1/156^2=1/60^2
ãªã©ååšã¯ãããæ¢ãããšãããšãªããªãèŠåŽããã
ããã§
1/a^2+1/b^2=1/c^2
ã®ä»ã®å®äŸãããã€ãçºèŠé¡ãã
äžæ¹
[2]a^2+b^2+c^2=d^2
ãæºããæŽæ°çµïŒa,b,c,d)ã¯
1^2+4^2+8^2=9^2
2^2+3^2+6^2=7^2
3^2+6^2+22^2=23^2
4^2+7^2+32^2=33^2
çã®æ§ã«
(a<b<cã§ãd=c+1ïŒ
ã§ã®ãã¿ãŒã³ãç䌌ãŠ
1/a^2+1/b^2+1/c^2=1/d^2
ãªã
1/7^2+1/14^2+1/21^2=1/6^2
1/9^2+1/18^2+1/72^2=1/8^2
1/13^2+1/39^2+1/52^2=1/12^2
1/19^2+1/57^2+1/342^2=1/18^2
1/31^2+1/155^2+1/186^2=1/30^2
ãªã©ã®æ§ã«
(ãã ãã0<a<b<c ã§d=a-1ïŒ
ã®æ¡ä»¶äžã§ã®ä»ã®å®äŸãæ¢ãåºããŠã»ããã
ããã«
[3]1/a^2+1/b^2+1/c^2+1/d^2=1/e^2
(ãã ãã0<a<b<c<d ã§e=a-1)
ã®äŸãäžã€ã¯èŠã€ããŠäžããã
No.2680GAI5æ20æ¥ 12:17
p^2+q^2=r^2 ãæãç«ã€ãšã
a=pr, b=qr, c=pq ãšããã°
1/a^2+1/b^2=1/c^2 ãæãç«ã¡ãŸããã
p^2+q^2=r^2ãæãç«ã€p,q,rã®äžè¬åŒã¯
p=m^2-n^2, q=2mn, r=m^2+n^2
ãšè¡šããŸãã®ã§ã
1/a^2+1/b^2=1/c^2ãæãç«ã€a,b,cã®äžè¬åŒã¯
a=(m^2-n^2)(m^2+n^2)=m^4-n^4
b=2mn(m^2+n^2)
c=2mn(m^2-n^2)
ãšè¡šããããšã«ãªããŸãã
åæ§ã«
p^2+q^2+r^2=s^2 ãæãç«ã€ãšã
a=pqs, b=prs, c=qrs, d=pqr ãšããã°
1/a^2+1/b^2+1/c^2=1/d^2 ãæãç«ã¡ã
p^2+q^2+r^2=s^2ã®äžè¬åŒã¯
p=|k^2+m^2-n^2|, q=2kn, r=2mn, s=k^2+m^2+n^2
ãšè¡šããŸãã
# ãã®åŒã®å€ãå
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# 蚌æããŠããŸããã®ã§ãããããããå
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1/a^2+1/b^2+1/c^2=1/d^2ã®äžè¬åŒã¯
a=2kn|k^2+m^2-n^2|(k^2+m^2+n^2)
b=2mn|k^2+m^2-n^2|(k^2+m^2+n^2)
c=4kmn^2(k^2+m^2+n^2)
d=4kmn^2|k^2+m^2-n^2|
ãå
±éå æ°ã§å²ã£ãŠ
a=k|k^2+m^2-n^2|(k^2+m^2+n^2)
b=m|k^2+m^2-n^2|(k^2+m^2+n^2)
c=2kmn(k^2+m^2+n^2)
d=2kmn|k^2+m^2-n^2|
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šè§£ãã©ããã¯ããããŸãããïŒè§£ã¯ãããã§ãçæã§ããŸããã
5é
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(k^2+l^2+m^2-n^2)^2+(2kn)^2+(2ln)^2+(2mn)^2=(k^2+l^2+m^2-n^2)^2
ã䜿ãã°åæ§ã«ã§ãããšæããŸãã
NEWNo.2681ãããã5æ20æ¥ 22:01
äžè¬åŒãäœãããšã¯æã£ãŠãã¿ãŸããã§ããã
ãã¿ãŽã©ã¹æ°ããã®ã¢ã¯ãããã£ãã¯ãªå€åœ¢ã®åŠæãæåããŸããã
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1/333^2+1/444^2+1/555^2+1/740^2+1/888^2+1/999^2=1/216^2(=1/6^6)
ãçºèŠããæã¯å°èºãããŠåã³ãŸããã
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1/62^2+1/93^2+1/155^2+1/186^2+1/217^2+1/279^2+1/434^2+1/465^2+1/651^2+1/930^2=1/45^2(=1/2025)
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ãã
p^2+q^2+r^2+s^2=t^2
ãæºããèªç¶æ°(p,q,r,s,t)
ãèŠã€ããŠããã°
a=p*q*r*t
b=q*r*s*t
c=r*s*p*t
d=s*p*q*t
ãšçœ®ãã°
1/a^2+1/b^2;1/c^2+1/d^2
=(1/(p*q*r)^2+1/(q*r*s)^2+1/(r*s*p)^2+1/(s*p*q)^2)/t^2
=(s^2+p^2+q^2+r^2)/(p*q*r*s)^2/t^2
=1/(p*q*r*s)^2
ãªã®ã§
e=p*q*r*sãšçœ®ãã°
1/a^2+1/b^2+1/c^2+1/d^2=1/e^2
ãæç«ããã
ããã«äžè¬çã«
(k^2+l^2+m^2-n^2)^2+(2*k*n)^2+(2*l*n)^2+(2*m*n)^2=(k^2+l^2+m^2+n^2)^2
ãæç«ããã®ã§
p=k^2+l^2+m^2-n^2
q=2*k*n
r=2*l*n
s=2*m*n
t=k^2+l^2+m^2+n^2
ãšçœ®ããŠããããäžã®a,b,c,d,eãžãããã代å
¥ããŠå
±éå å4*k*n^2ãæããš
a(k.l.m,n)=l*((k^2+l^2+m^2)^2-n^4)
b(k,l,m,n)=2*l*m*n*(k^2+l^2+m^2+n^2)
c(k,l,m,n)=l*m*((k^2+l^2+m^2)^2-n^4)
d(k,l,m,n)=m*((k^2+l^2+m^2)^2-n^4)
e(k,l,m,n)=2*l*m*n*(k^2+l^2+m^2-n^2)
ã«ãªããšæãã
ããã§
a(2,2,3,4)=66
b(2,2,3,4)=1584
c(2,2,3,4)=198
d(2,2,3,4)=99
e(2,2,3,4)=48
ãšããã
1/66^2+1/1584^2+1/198^2+1/99^2=299/836352
ãšãªã
1/48^2=1/2304
ãšäžèŽããªãïŒ
ãããäœæ
çºçããã®ãïŒ
ãŸã
1/4^2=1/5^2+1/7^2+1/28^2+1/35^2
ãèµ·ããã®ã§ããããã®åŒã¯äžã®å
¬åŒã§æ±ãŸãã®ã§ããããïŒ
NEWNo.2682GAI仿¥ 08:05
æåŸã®3è¡ãé€ãåç
> å
±éå å4*k*n^2ãæããš
c=r*s*p*tã¯kã§å²ãåããªããšæããŸãã
ãã£ãŠå
±éå åã¯4*n^2ã§ãããæ£ããã¯
a(k,l,m,n)=l*k*((k^2+l^2+m^2)^2-n^4)
b(k,l,m,n)=2*k*l*m*n*(k^2+l^2+m^2+n^2)
c(k,l,m,n)=l*m*((k^2+l^2+m^2)^2-n^4)
d(k,l,m,n)=k*m*((k^2+l^2+m^2)^2-n^4)
e(k,l,m,n)=2*k*l*m*n*(k^2+l^2+m^2-n^2)
ãšãªããããã«ãã£ãŠèšç®ããã
a(2,2,3,4)=132
b(2,2,3,4)=3168
c(2,2,3,4)=198
d(2,2,3,4)=198
e(2,2,3,4)=96
ãã
1/132^2+1/3168^2+1/198^2+1/198^2=1/96^2
ãæãç«ã€ããšãããããŸãã
NEWNo.2683ãããã仿¥ 12:38
æåŸã®3è¡ã®åç
> ãŸã
> 1/4^2=1/5^2+1/7^2+1/28^2+1/35^2
> ãèµ·ããã®ã§ããããã®åŒã¯äžã®å
¬åŒã§æ±ãŸãã®ã§ããããïŒ
a(k,l,m,n)=l*k*|(k^2+l^2+m^2)^2-n^4|
b(k,l,m,n)=2*k*l*m*n*(k^2+l^2+m^2+n^2)
c(k,l,m,n)=l*m*|(k^2+l^2+m^2)^2-n^4|
d(k,l,m,n)=k*m*|(k^2+l^2+m^2)^2-n^4|
e(k,l,m,n)=2*k*l*m*n*|k^2+l^2+m^2-n^2|
ã®ããã«è² ã«ãªããªãããã«çµ¶å¯Ÿå€ãä»ããŠããã°ã
a(2,10,14,20)=1400000
b(2,10,14,20)=7840000
c(2,10,14,20)=9800000
d(2,10,14,20)=1960000
e(2,10,14,20)=1120000
ãšãªãããããæå€§å
¬çŽæ°ã®280000ã§å²ãã°
(a,b,c,d,e)=(5,28,35,7,4)ãåŸãããŸããã
NEWNo.2685ãããã仿¥ 13:54
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ä¿®æ£ããŠããããæ±ãŸã(a,b,c,d,e)ã®5çµãç¹æ€ããŠããããå€ãã®å Žåå
±éã®æ°ãå«ãããšãèµ·ããããã
ç°ãªã5åã«éå®ããŠãããe=1~1000ã®éã«ã¯å
ãã«20ãã¿ãŒã³ã»ã©ãããªããç¹ã«e=960ã§ã¯
1/1008^2+1/3360^2+1/10080^2+1/20160^2=1/960^2
1/1296^2+1/1728^2+1/2592^2+1/12960^2=1/960^2
1/1260^2+1/1680^2+1/4032^2+1/5040^2=1/960^2
1/1290^2+1/1548^2+1/3870^2+1/123840^2=1/960^2
1/1206^2+1/1608^2+1/9648^2+1/192960^2=1/960^2
ã®æ§ã«5éããäœãæ¹ãçºçããã
ããå°ãå°ãªãæ°ã§ã¯
1/23^2+1/46^2+1/92^2+1/230^2=1/20^2
1/46^2+1/92^2+1/184^2=1/460^2=1/40^2
1/62^2+1/310^2+1/465^2+1/620^2=1/60^2
1/74^2+1/148^2+1/185^2+1/222^2=1/60^2
1/148^2+1/296^2+1/370^2+1/444^2=1/120^2
1/155^2+1/248^2+1/310^2+1/930^2=1/120^2
1/185^2+1/370^2+1/740^2+1/1184^2=1/160^2
1/222^2+1/444^2+1/555^2+1/666^2=1/180^2
ãªã©ãèµ·ããŸããã
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¬åŒããçºçå¯èœãªã®ã§ããã
NEWNo.2686GAI仿¥ 14:23
1/23^2+1/46^2+1/92^2+1/230^2=1/20^2 㯠(k,l,m,n)=(1,2,4,5)
1/46^2+1/92^2+1/184^2=1/460^2=1/40^2 㯠å¯çŽ(äžã®2å)
1/62^2+1/310^2+1/465^2+1/620^2=1/60^2 㯠(k,l,m,n)=(2,3,15,14)
1/74^2+1/148^2+1/185^2+1/222^2=1/60^2 㯠(k,l,m,n)=(2,3,6,5)
1/148^2+1/296^2+1/370^2+1/444^2=1/120^2 㯠å¯çŽ(äžã®2å)
1/155^2+1/248^2+1/310^2+1/930^2=1/120^2 㯠(k,l,m,n)=(1,3,6,4)
1/185^2+1/370^2+1/740^2+1/1184^2=1/160^2 㯠(k,l,m,n)=(1,2,4,4)
1/222^2+1/444^2+1/555^2+1/666^2=1/180^2 㯠å¯çŽ(4ã€äžã®3å)
ã§ããã
ãããã1/4^2=1/5^2+1/7^2+1/28^2+1/35^2 㯠(k,l,m,n)=(1,5,7,10) ã§ååã§ããã
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NEWNo.2687ãããã仿¥ 15:54
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No.2443Tabasco1æ2æ¥ 14:51
åäœååšäžã®nç¹ããz_1,z_2, ⊠,z_n ãšãã
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åŒ
P(w)=(w-z_1)*(w-z_2)*âŠ*(w-z_n)
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|P(w)|â§2 ã〠1â§|w| ãªã w ã®ååšã次ã®ããã«ããŠç€ºããã
(z_1)*(z_2)*âŠ*(z_n)=(-1)^n ãšãªãããã«åº§æšãèšå®ã§ããã
k=1,2,âŠ,nã«å¯ŸããŠãw_k=exp(i*2*Ï*k/n) ãšãããšã
P(w_1)+P(w_2)+âŠ+P(w_n)=2*n
ã§ããããšããããããã£ãŠã
|P(w_1)|+|P(w_2)|+âŠ+|P(w_n)|â§2*n.
ãã£ãŠã|P(w_1)|ïŒ|P(w_2)|ïŒâŠïŒ|P(w_n)|ã®ãã¡ã
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No.2445at1æ5æ¥ 18:00
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No.2446Dengan kesaktian Indukmu1æ6æ¥ 14:37
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No.2448DD++1æ9æ¥ 21:42
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No.2462Dengan kesaktian Indukmu1æ21æ¥ 10:17
1ã®åå§(n+1)乿 ¹ãzãšãããšãz^(n+1)=1ã§ãz^i(i=0,1,2,...,n)ã¯è€çŽ æ°å¹³é¢äžã§æ£(n+1)è§åœ¢ãšãªããŸãã
zã®è€çŽ å
±åœ¹z^*ã¯z^*=z^-1ãªã®ã§ãå®è»žäžã®ç¹(x,0)ãšz^i(i=1,2,...,n)ãšã®è·é¢ã®ç©ã®2ä¹ã¯ã
(x-z)*(x-z^-1)*(x-z^2)*(x-z^-2)*...*(x-z^n)*(x-z^-n)
=(x-z)*(x-z^n)*(x-z^2)*(x-z^(n-1))*...*(x-z^n)*(x-z)
=((x-z)*(x-z^2)*...(x-z^n))^2
ãšãªããŸãã
(x-1)*(x-z)*(x-z^2)*..(x-z^n)=x^(n+1)-1=(x-1)*(x^n+...x^2+x+1)
ãªã®ã§ã
(x-z)*(x-z^2)*...(x-z^n)=x^n+...x^2+x+1
ãšè¡šãããšãã§ããŠãå®è»žäžã®ç¹(x,0)ãšz^i(i=1,2,...,n)ãšã®è·é¢ã®ç©ã¯
|x^n+...x^2+x+1|
ãšãªããŸãã
x=1ã®ãšãã¯ã
x^n+...x^2+x+1=n+1
ãšãªã£ãŠãè·é¢ã®ç©ã¯n+1ãšãªããŸãã
x=0ã®ãšãã¯ã(0,0)ãšz^i(i=1,2,...,n)ãšã®è·é¢ã¯1ãªã®ã§ããããã®ç©ãæããã«1ã§ããã
((-z)*(-z^2)*...*(z^n))^2=(-z)^(n(n+1)/2*2)=(-z)^(n(n+1))
=(-1)^(n(n+1))*z^(n(n+1))=1*1=1
ãšãªãã®ã§ãè·é¢ã®ç©ã¯1ãšãªããŸãã
å®è»žäžã®ç¹(x,0)ãšz^i(i=1,2,...,n)ãšã®è·é¢ã®ç©|x^n+...x^2+x+1|ã¯xã«ã€ããŠé£ç¶ãªå®æ°å€é¢æ°ãªã®ã§ã
äžéå€ã®å®çãããè·é¢ã®ç©ã2ãšãªãç¹ã¯(0,0)ãš(1,0)ã®éã«ããããšã«ãªããŸãã
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1ã®åå§(2k+1)乿 ¹ãzãšãããšãz^(2k+1)=1ã§ãz^i(i=0,1,...,2k)ã¯è€çŽ æ°å¹³é¢äžã§æ£(2k+1)è§åœ¢ãšãªããŸãã
å®è»žäžã®ç¹(x,0)ãšz^i(i=0,1,...,2k)ãšã®è·é¢ã®ç©ã®2ä¹ã¯ã
(x-1)^2*(x-z)*(x-z^-1)*(x-z^2)*(x-z^-2)*...*(x-z^2k)*(x-z^-2k)
=((x-1)*(x-z)*(x-z^2)*...(x-z^2k))^2
=(x^(2k+1)-1)^2
ãšãªããŸãã
x=-1ã®ãšãã
(x^(2k+1)-1)^2=(-2)^2=4
ãšãªãã®ã§ã(-1,0)ãšz^i(i=0,1,...,2k)ãšã®è·é¢ã®ç©ã¯2ãšãªããŸãã
--------------------------------------------------------------
1ã®åå§2k乿 ¹ãzãåå§4k乿 ¹ãwãšãããšãn=2k,w^2=z,w^4k=z^2k=1ã§ãw^i(i=0,1,...,4k-1)ã¯è€çŽ æ°å¹³é¢äžã§æ£4kè§åœ¢ãšãªããw^(2i+1)(i=0,1,...,2k-1)ã¯è€çŽ æ°å¹³é¢äžã§æ£2kè§åœ¢ãšãªããŸãã
å®è»žäžã®ç¹(x,0)ãšw^(2i+1)(i=0,1,...,2k-1)ãšã®è·é¢ã®ç©ã®2ä¹ã¯ã
(x-w)*(x-w^-1)*(x-w^3)*(x-w^-3)*...*(x-w^(4k-1))*(x-w^-(4k-1))
=(x-w)*(x-w^(4k-1))*(x-w^3)*(x-w^(4k-3))*...*(x-w^(4k-1))*(x-w)
=((x-w)*(x-w^3)*...*(x-w^(4k-1)))^2
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No.2656moonlight4æ29æ¥ 20:36
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No.2658DD++4æ29æ¥ 21:43
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2797793, 895375, 368825, 152326, 55475, 16989, 4315, 889, 142, 16
895375, 1886974, 858064, 400591, 167993, 59769, 17877, 4456, 904, 142
368825, 858064, 1553894, 840565, 413847, 172825, 60764, 18016, 4456, 889
152326, 400591, 840565, 1388969, 834802, 418154, 173782, 60764, 17877, 4315
55475, 167993, 413847, 834802, 1318601, 833690, 418154, 172825, 59769, 16989
16989, 59769, 172825, 418154, 833690, 1318601, 834802, 413847, 167993, 55475
4315, 17877, 60764, 173782, 418154, 834802, 1388969, 840565, 400591, 152326
889, 4456, 18016, 60764, 172825, 413847, 840565, 1553894, 858064, 368825
142, 904, 4456, 17877, 59769, 167993, 400591, 858064, 1886974, 895375
16, 142, 889, 4315, 16989, 55475, 152326, 368825, 895375, 2797793
total: 4292145(éã)
暪ç·ç·æ°20;(åèª2æ¬ãã€åæã«æšªç·ãæžãå
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1206969885175, 444626687408, 223944116341, 123985414511, 68419073997, 35219432968, 16356793415, 6802760919, 2521009672, 809262504
444626687408, 736976131952, 404974329652, 244129892658, 146778115239, 82292337422, 41427338639, 18559662466, 7368931802, 2521009672
223944116341, 404974329652, 552089840963, 377497635883, 254748110156, 159277066729, 88500743423, 43260170378, 18559662466, 6802760919
123985414511, 244129892658, 377497635883, 454051817726, 360453569477, 259933003640, 163318227538, 88500743423, 41427338639, 16356793415
68419073997, 146778115239, 254748110156, 360453569477, 407940958106, 354592769176, 259933003640, 159277066729, 82292337422, 35219432968
35219432968, 82292337422, 159277066729, 259933003640, 354592769176, 407940958106, 360453569477, 254748110156, 146778115239, 68419073997
16356793415, 41427338639, 88500743423, 163318227538, 259933003640, 360453569477, 454051817726, 377497635883, 244129892658, 123985414511
6802760919, 18559662466, 43260170378, 88500743423, 159277066729, 254748110156, 377497635883, 552089840963, 404974329652, 223944116341
2521009672, 7368931802, 18559662466, 41427338639, 82292337422, 146778115239, 244129892658, 404974329652, 736976131952, 444626687408
809262504, 2521009672, 6802760919, 16356793415, 35219432968, 68419073997, 123985414511, 223944116341, 444626687408, 1206969885175
total: 2129654436910(éã)
暪ç·ç·æ°30;;(åèª3æ¬ãã€æžãå
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496647560097440001, 200445588666012991, 111899880246277899, 69792696535021405, 44738672491416379, 27922874500844965, 16258458172179943, 8597168046702841, 4054782107743644, 1643303416611824
200445588666012991, 282712254410516606, 174876883331777285, 118941996483630956, 82376641820193608, 55272922570250507, 34417898391400316, 19315501555853237, 9586514942872742, 4054782107743644
111899880246277899, 174876883331777285, 203125589064861508, 157132397723195171, 120882336138695072, 89132275101361093, 60473442328480160, 36565510743047626, 19315501555853237, 8597168046702841
69792696535021405, 118941996483630956, 157132397723195171, 166300290157052329, 146258783232882355, 121111693187082065, 91313328069327192, 60473442328480160, 34417898391400316, 16258458172179943
44738672491416379, 82376641820193608, 120882336138695072, 146258783232882355, 151780229152448736, 142524556085077112, 121111693187082065, 89132275101361093, 55272922570250507, 27922874500844965
27922874500844965, 55272922570250507, 89132275101361093, 121111693187082065, 142524556085077112, 151780229152448736, 146258783232882355, 120882336138695072, 82376641820193608, 44738672491416379
16258458172179943, 34417898391400316, 60473442328480160, 91313328069327192, 121111693187082065, 146258783232882355, 166300290157052329, 157132397723195171, 118941996483630956, 69792696535021405
8597168046702841, 19315501555853237, 36565510743047626, 60473442328480160, 89132275101361093, 120882336138695072, 157132397723195171, 203125589064861508, 174876883331777285, 111899880246277899
4054782107743644, 9586514942872742, 19315501555853237, 34417898391400316, 55272922570250507, 82376641820193608, 118941996483630956, 174876883331777285, 282712254410516606, 200445588666012991
1643303416611824, 4054782107743644, 8597168046702841, 16258458172179943, 27922874500844965, 44738672491416379, 69792696535021405, 111899880246277899, 200445588666012991, 496647560097440001
total: 982000984280251892(éã)
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for(n=1,9,print(2*n+2";"subst(polchebyshev(2*n+2,2),x,t/2)))
4;t^4 - 3*t^2 + 1
6;t^6 - 5*t^4 + 6*t^2 - 1
8;t^8 - 7*t^6 + 15*t^4 - 10*t^2 + 1
10;t^10 - 9*t^8 + 28*t^6 - 35*t^4 + 15*t^2 - 1
12;t^12 - 11*t^10 + 45*t^8 - 84*t^6 + 70*t^4 - 21*t^2 + 1
14;t^14 - 13*t^12 + 66*t^10 - 165*t^8 + 210*t^6 - 126*t^4 + 28*t^2 - 1
16;t^16 - 15*t^14 + 91*t^12 - 286*t^10 + 495*t^8 - 462*t^6 + 210*t^4 - 36*t^2 + 1
18;t^18 - 17*t^16 + 120*t^14 - 455*t^12 + 1001*t^10 - 1287*t^8 + 924*t^6 - 330*t^4 + 45*t^2 - 1
20;t^20 - 19*t^18 + 153*t^16 - 680*t^14 + 1820*t^12 - 3003*t^10 + 3003*t^8 - 1716*t^6 + 495*t^4 - 55*t^2 + 1
ããã§çžŠç·ã4æ¬ã®æã¯
t^4-3*t^2+1=X^2-3*X+1
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T4(k)=3*T4(k-1)-T4(k-2)
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䜿ãããã«ã¯T4(1)=3,T4(2)=8ãäžããã°è¯ãã
ãã瞊ç·ã20æ¬ãªã
T20(k)=19*T20(k-1)-153*T20(k-2)+680*T20(k-3)-1820*T20(k-4)+3003*T20(k-5)+1716*T20(k-6)-495*T20(k-7)+55*T20(k-8)-T20(k-9)
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T20(1)=19,T20(2)=208,T20(3)=1725,T20(4)=12051,T20(5)=74907,T20(6)=427924,T20(7)=2294248,T20(8)=11709940,T20(9)=57483052,T20(10)=273438880
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gp > for(n=1,9,print(2*n+3";"subst(polchebyshev(2*n+3,2),x,t/2)/t))ãã
5;t^4 - 4*t^2 + 3
7;t^6 - 6*t^4 + 10*t^2 - 4
9;t^8 - 8*t^6 + 21*t^4 - 20*t^2 + 5
11;t^10 - 10*t^8 + 36*t^6 - 56*t^4 + 35*t^2 - 6
13;t^12 - 12*t^10 + 55*t^8 - 120*t^6 + 126*t^4 - 56*t^2 + 7
15;t^14 - 14*t^12 + 78*t^10 - 220*t^8 + 330*t^6 - 252*t^4 + 84*t^2 - 8
17;t^16 - 16*t^14 + 105*t^12 - 364*t^10 + 715*t^8 - 792*t^6 + 462*t^4 - 120*t^2 + 9
19;t^18 - 18*t^16 + 136*t^14 - 560*t^12 + 1365*t^10 - 2002*t^8 + 1716*t^6 - 792*t^4 + 165*t^2 - 10
21;t^20 - 20*t^18 + 171*t^16 - 816*t^14 + 2380*t^12 - 4368*t^10 + 5005*t^8 - 3432*t^6 + 1287*t^4 - 220*t^2 + 11
ããããäŸãã°çžŠç·ã17æ¬ãªã
T17(k)=16*T17(k-1)-105*T17(k-2)+364*T17ïŒk-3)-715*T17(k-4)+792*T17(k-5)-462*T17(k-6)+120*T17(k-7)-9*T17(k-8) ãš
T17(1)=16,T17(2)=151,T17(3)=1100,T17(4)=6854,T17(5)=38480,T17(6)=200655,T17(7)=990756,T17(8)=4692780
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1;16
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3;1100
4;6854
5;38480
6;200655
7;990756
8;4692780
9;21518464
10;96160636
11;420866416
12;1810911128
13;7683058880
14;32215438277
15;133749903324
16;550649378199
17;2250829575120
18;9143995148926
19;36950585233432
20;148629592843159
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No.2653moonlight4æ29æ¥ 12:16
claudeã«ããã°ã©ã ã®è§£èª¬ããé¡ãããŠã¿ãŸããã
Juliaã«æžãæãããã®ã解説ããŠè²°ã£ãŠããŸããã¢ã«ãŽãªãºã çã«ã¯åãäºã§ãããã
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ãã¿ã ãããæ°ããããã°ã©ã ã®ã¢ã«ãŽãªãºã ã«ã€ããŠã颿°ããšã«è§£èª¬ããŸãã
ãã®ããã°ã©ã ã¯ããã¿ã ããã®å¯èœãªçµã¿åããæ°ïŒãŸãã¯çµè·¯æ°ïŒãèšç®ãããã®ã§ããå颿°ã®åœ¹å²ãšèåŸã«ããã¢ã«ãŽãªãºã ã説æããŸãïŒ
count_amidakuji(n, m) 颿°
ãã®é¢æ°ã¯å
šäœã®åŠçã管çããŠããã以äžã®ãããªã¹ãããã§åäœããŸãïŒ
åæå:
næ¬ã®çžŠç·ãšãããããæšªç·ã§ã€ãªãæ§é ãèããŸã
3次å
é
å a[i, j, k] ãäœæããŸãïŒ
i: 暪ç·ã®å±€ã衚ããŸãïŒ1ããn-1ãŸã§ïŒ
j: åºçºç¹ã衚ããŸãïŒ1ããnãŸã§ïŒ
k: å°éç¹ã衚ããŸãïŒ1ããnãŸã§ïŒ
æåã¯ãa[1, j, j] = 1 ãšããŠãåºçºç¹jããåãäœçœ®jã«å°éããçµè·¯ã1ã€ããããšã衚ããŸã
å埩æäœïŒmåïŒ:
åå埩ã¯ã暪ç·ïŒãã¿ã ããã®ã暪æ£ãïŒã1æ¬è¿œå ããå¯èœæ§ãã·ãã¥ã¬ãŒã·ã§ã³ããŸã
倧ããåããŠã环ç©ãã§ãŒãºããšã亀æãã§ãŒãºãããããŸãïŒ
a. 环ç©ãã§ãŒãº:
next[1, j, k] ã¯ãæåã®å±€ãš2çªç®ã®å±€ã®å€ãåèšããŸã
äžé局㮠next[i, j, k] ã¯ãåã®å±€ããã®çޝç©å€ã𿬡ã®å±€ã®çŸåšå€ãåèšããŸã
ããã«ãããçµè·¯æ°ãäžããäžãžãšçޝç©ãããŠãããŸã
b. 亀æãã§ãŒãº:
åå±€iã«ãããŠãäœçœ®(j,i)ãš(j,i+1)ã®å€ã亀æããŸã
ããã¯ã暪ç·ãåŒããããšãã«çµè·¯ãã©ã®ããã«å€åãããã衚çŸããŠããŸã
æçµèšç®:
ãã¹ãŠã®å埩ãçµãã£ãããååºçºç¹jããåå°éç¹kãžã®çµè·¯æ°ã®åèšãèšç®ããŸã
ç¹ã«æåŸã®åïŒk=nïŒãžã®çµè·¯ã®ç·æ°ããtotalããšããŠèšç®ãããŸã
main() 颿°
ãã®é¢æ°ã¯åã«ãŠãŒã¶ãŒã€ã³ã¿ãŒãã§ãŒã¹ãæäŸããŸãïŒ
ãŠãŒã¶ãŒããå
¥åå€nïŒçžŠç·ã®æ¬æ°ïŒãšmïŒæšªç·ã®è¿œå åæ°ïŒãåãåããŸã
倧ããªèšç®ã«ãªãå Žåã®èŠåã衚瀺ããŸã
count_amidakuji(n, m) ãåŒã³åºããŠèšç®ãå®è¡ããŸã
ã¢ã«ãŽãªãºã ã®æ°åŠçè§£é
ãã®ã¢ã«ãŽãªãºã ã¯ããã¿ã ããã®çµã¿åãããçŽæ¥çæããã®ã§ã¯ãªããåçèšç»æ³ã䜿çšããŠçµè·¯æ°ãå¹ççã«èšç®ããŠããŸãïŒ
é
å a[i, j, k] ã¯ãiå±€ç®ã§åºçºç¹jããå°éç¹kãžã®çµè·¯æ°ã衚ããŸã
暪ç·ãåŒããããšã飿¥ããçµè·¯ã亀æãããŸãïŒäº€æãã§ãŒãºïŒ
å±€ã远å ãããããšã«ãçµè·¯æ°ã¯çޝç©ãããŸãïŒçޝç©ãã§ãŒãºïŒ
måã®å埩åŸãæçµçãªçµè·¯æ°ãèšç®ãããŸã
ç¹ã«ãã®ã¢ã«ãŽãªãºã ã¯ããã¿ã ããããæä»çãªæšªç·ã®çµã¿åããããšããŠå¹ççã«ã«ãŠã³ãããŠããŸãããã¹ãŠã®å¯èœãªçµã¿åãããåæããã®ã§ã¯ãªããæ°åŠçã«çµè·¯æ°ãèšç®ããã®ã§ã倧ããªå
¥åå€ã«å¯ŸããŠãæ¯èŒçå¹ççã«åäœããŸãã
ãã ããæéèšç®éã¯O(mÃn³)ãªã®ã§ãéåžžã«å€§ããªå€ã«å¯ŸããŠã¯èšç®æéãé·ããªãå ŽåããããŸããããã«å¯Ÿå¿ãããããBigIntåã䜿çšããŠæ°å€ã®ãªãŒããŒãããŒãé²ãã§ããŸãã
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äœãšãªããæŒžååŒçããšè¡šçŸããŠããŸããã, ãåçèšç»æ³ããšåŒã¶ã®ã§ããã
説æã¯æœè±¡çã§ããå€å°ã¯åããæãã®ã§ç¢ºèªããŠã¿ãŸãã
No.2654moonlight4æ29æ¥ 12:46
> 倧ããªèšç®ã«ãªãå Žåã®èŠåã衚瀺ããŸã
ããã¯ïŒAIãäœãè¶³ããã®ã§ãªããã°ïŒn>2 ã§ãªãã£ãå Žåã®èŠåã®ããšã§ãããïŒ
ããã¯å€§ããªèšç®ã«ãªãããã§ã¯ãªããn=2 ã ãšéäžã§ã¯ã©ãã·ã¥ããã®ã§å
¥ããŠããŸãã
n=2 ã®å Žåã¯æããã«1éããããªãã®ã§ãç¹å¥å¯Ÿå¿ãã䟡å€ããããŸãããã
ãã以å€ã¯AIã®è§£éã§ãã£ãŠããŸãã
æ¹éã¯ã挞ååŒã§ãã£ãŠãŸããã
DPïŒåçèšç»æ³ïŒâ挞ååŒããªã®ã§ãDPãšåŒãã§ãããã ãã§ãã
No.2655DD++4æ29æ¥ 13:52
æè¿ãŸããçµ±èšã絡ã¿ã§ããã¿ã ãããã®ã©ããéžã¶ãã¯åããããç³»ã®è©±ã沞ããŠããŸãã
æ°ã«ãªãèšäºããã£ãã®ã§ã確ããããããšããŸããã, ããããããã¿ã ãããã®æ°ãäžããå€ããªãããšã«æ°ãã€ããŸããã
仿¹ããªãã®ã§æ°ããŠã¿ãããšããã®ã§ãã...
äŸãã°, 瞊ã®çã4æ¬ã§, 暪æ£ã3æ¬ã®å Žåã«20éããïŒãšãªã£ãã®ã§ãã, ã©ãã«ãèªä¿¡ãæãŠãŸããã
ãã , 暪æ£ã3æ¬ã®å Žåã§, 瞊ã®çã®æ¬æ°ãå¢ãããŠããã°, 䌌ãèšç®ã§æŒžååŒçã«æ°ãããããã ãš...
ã§ããã£ã±ãèŠé ãåŸãªãã®ã§, äŸãã°ã瞊ã®çã5æ¬ã§æšªæ£ã6æ¬å
¥ã£ããã¿ã ãããã®ç·æ°ã¯ã©ãèšç®ããã°è¯ããæããŠäžãããªã
No.2613moonlight4æ23æ¥ 21:13
ã20éããã®æ°ãããã§ããå·Šã«1æ¬ãäžã«0æ¬ãå³ã«2æ¬ããæ°ããããŠããªãæ°ãããŸãã
ç§ã®åéãã§ãããã容赊äžããã
No.2614ãããã4æ23æ¥ 21:59
èªåããã¿ã ããã«ã€ããŠããã€ãã®æçš¿ãããŠããã®ãèšæ¶ããŠããã®ã§èª¿ã¹ãŠã¿ãã
ç§ã®åå¿é²äžã®
æ°åŠã»ã»ã»ãã®ä»(æ°åŠã«ã€ããŠã®éåŠãã»ã»ã»)
æãéãã®ãã¿ã ãããäœãæ¹æ³ã(å³åäžãã2çªç®)
ã«é¢é£èšäºããŸãšããããŠããŸãã
æãããã£ãã®ã§èªåã§ããããäžåºŠæŽçããŠã¿ãŸããã
瞊ç·ã4æ¬ã§æšªç·ãnæ¬ã§ã¯(A088305)
gp > a(n)=(((3+sqrt(5))/2)^(n+1)-((3-sqrt(5))/2)^(n+1))/sqrt(5)
gp > for(n=1,10,print(n";"round(a(n))))
1;3
2;8
3;21
4;55
5;144
6;377
7;987
8;2584
9;6765
10;17711
瞊ç·ã5æ¬ã§æšªç·ãnæ¬ã§ã¯(A261547)
gp > b(n)=(3^(n+1)-1)/2
gp > for(n=1,10,print(n";"b(n)))
1;4
2;13
3;40
4;121
5;364
6;1093
7;3280
8;9841
9;29524
10;88573
瞊ç·ã6æ¬ã§æšªç·ãnæ¬ã§ã¯(A005021)
c(n)={S=[];}for(i=0,n,for(j=0,n-i,for(k=0,n-i-j,\
S=concat(S,[binomial(i+j,j)*binomial(j+k,k)*binomial(n+1-j,n-(i+j+k))]))));vecsum(S)
gp > for(n=1,10,print(n";"c(n)))
1;5
2;19
3;66
4;221
5;728
6;2380
7;7753
8;25213
9;81927
10;266110
ãªã瞊æ£ã6æ¬ã§ã®æšªè»žnæ¬ã§ã®ãã¿ã ããã®æ¬æ°ãA005021ã§ã®è§£èª¬ã§ã¯
P_6ãšåŒã°ããéïŒçŽç·äžïŒç¹AãBãCãDãEãF ã䞊ãã§ãããïŒããAããåºçºãã
2*n+5(æ©)ã«ãŠFã®å°ç¹ã«å°çããé
æ©ã®ã³ãŒã¹ãäœéãã§ãããïŒ ããã«åããšããã
ãã£ãŠæšªæ£2æ¬ã§ã¯2*2+5=9æ©ã§é²ãå®äŸãæ§æãããš
1;[A, B, A, B, A, B, C, D, E, F]
2;[A, B, A, B, C, B, C, D, E, F]
3;[A, B, A, B, C, D, C, D, E, F]
4;[A, B, A, B, C, D, E, D, E, F]
5;[A, B, A, B, C, D, E, F, E, F]
6;[A, B, C, B, A, B, C, D, E, F]
7;[A, B, C, B, C, B, C, D, E, F]
8;[A, B, C, B, C, D, C, D, E, F]
9;[A, B, C, B, C, D, E, D, E, F]
10;[A, B, C, B, C, D, E, F, E, F]
11;[A, B, C, D, C, B, C, D, E, F]
12;[A, B, C, D, C, D, C, D, E, F]
13;[A, B, C, D, C, D, E, D, E, F]
14;[A, B, C, D, C, D, E, F, E, F]
15;[A, B, C, D, E, D, C, D, E, F]
16;[A, B, C, D, E, D, E, D, E, F]
17;[A, B, C, D, E, D, E, F, E, F]
18;[A, B, C, D, E, F, E, D, E, F]
19;[A, B, C, D, E, F, E, F, E, F]
ãšèšç®ã®éã19ãã¿ãŒã³æ§æå¯èœãªã®ã§
瞊æ£ã5æ¬ã§ããæã¯
P_5ãšåŒã°ããéïŒçŽç·äž5ç¹AãBãCãDãE ã䞊ãã§ãããïŒããAããåºçºãã
2*n+4(æ©)ã«ãŠEã®å°ç¹ã«å°çããé
æ©ã®ã³ãŒã¹ãäœéãã§ãããïŒ
ãšäžã®ãã¿ãŒã³ãåèã«
ä»åºŠã¯2*2+4=8æ©ã§é²ã¿
1;[A, B, A, B, A, B, C, D, E]
2;[A, B, A, B, C, B, C, D, E]
3;[A, B, A, B, C, D, C, D, E]
4;[A, B, A, B, C, D, E, D, E]
5;[A, B, C, B, A, B, C, D, E]
6;[A, B, C, B, C, B, C, D, E]
7;[A, B, C, B, C, D, C, D, E]
8;[A, B, C, B, C, D, E, D, E]
9;[A, B, C, D, C, B, C, D, E]
10;[A, B, C, D, C, D, C, D, E]
11;[A, B, C, D, C, D, E, D, E]
12;[A, B, C, D, E, D, C, D, E]
13;[A, B, C, D, E, D, E, D, E]
ã®13éãïŒèšç®äžäžèŽ)
ãããã«æ¢ãããšãã§ããŸãã
ã ãã瞊æ£4æ¬ã®ãšãã¯
P_4ãšåŒã°ããéïŒçŽç·äž4ç¹AãBãCãD ã䞊ãã§ãããïŒããAããåºçºãã
2*n+3(æ©)ã«ãŠDã®å°ç¹ã«å°çããé
æ©ã®ã³ãŒã¹ãäœéãã§ãããïŒ
ã§åŠçãããæšªæ£2æ¬ã§ã¯7æ©ã§é²ã¿
1;[A, B, A, B, A, B, C, D]
2;[A, B, A, B, C, B, C, D]
3;[A, B, A, B, C, D, C, D]
4;[A, B, C, B, A, B, C, D]
5;[A, B, C, B, C, B, C, D]
6;[A, B, C, B, C, D, C, D]
7;[A, B, C, D, C, B, C, D]
8;[A, B, C, D, C, D, C, D]
ãèŠã€ããã
No.2615GAI4æ23æ¥ 23:41
ããããšãããããŸãã
ãã£ããæ°ãèœãšããããŠããäºã確èªã§ããŸããã
è¡ãã€æ»ãã€ã®é è·¯æ°ã§æ°ããããçè·¯ã¯ã¡ãããšç¢ºèªã§ããŠãŸããããPythonã§ããã°ã©ã ããŠã¿ãŠç¢ºãã«æžãããŠããå Žåãªæ°ãåŸãããäºã¯åãããŸããã
次ã¯èšäºã«ãã£ãã瞊æ£8æ¬æšªæ£12æ¬ã®å Žåã«ããã¿ã ããã®è¡ãå
ãå ŽåããããŠæ°ããäºãå¿
èŠã«ãªããŸãã
ãè¡ãã€æ»ãã€ãã1ãš-1ã®ãªã¹ãã§æ°ãäžããäºã¯ã§ããã®ã§ãããšã¯ãã®ãªã¹ããããã¿ã ããã埩å
ããŠè¡ãå
ã確èªããã°è¯ãã®ã§ãã... ãã¿ã ããã®ã埩å
ãã¯ã©ã®ããã«ããã°è¯ãã§ãããïŒ
No.2616moonlight4æ24æ¥ 11:51
瞊8æ¬ã§æšªæ£næ¬ã®ãšãã®ç°ãªããã¿ã ããã®åŒãæ¹ã¯
次ã®èšç®ã§äžãããããã§ãã
gp > F(n)={S=[];}for(i=0,n,for(j=0,n-i,for(k=0,n-i-j,for(l=0,n-i-j-k,for(m=0,n-i-j-k-l,
W=binomial(i+j,j)*binomial(j+k,k)*binomial(k+l,l)*binomial(l+m,m)*binomial(n+1-(j+k+l),n-(i+j+k+l+m));
S=concat(S,[W]))))));vecsum(S)
gp > for(n=1,12,print(n";"F(n)))
1;7
2;34
3;143
4;560
5;2108
6;7752
7;28101
8;100947
9;360526
10;1282735
11;4552624
12;16131656
OEISã§æ€çŽ¢ãããšA005023ããããããŸããã
åŸã£ãŠæ±ããã¹ãå€ã¯16131656(éã)ã§ã¯ïŒ
ç§ãé
æ©ãšãã¿ã ããã察å¿ãããããšè©Šã¿ãã®ã§ããç·æ°ã§äžèŽããèšããªãã§ãã
No.2617GAI4æ24æ¥ 14:03
察å¿ã®ä»æ¹ã¯ãããããªããïŒãšãããã®ã«æãè³ããŸãããåŠäœã§ãããã
ããšã¯ä»æ¹ãªãã®ã§, Pythonã§äžã€äžã€æ°ãããã...
No.2618moonlight4æ24æ¥ 19:01
以äžã®èãã¯ã©ãã§ããããïŒ
næ¬ã®çžŠç·ã«mæ¬ã®æšªç·ãåŒãå Žåã
ã»é
æ°m
ã»åé
ã®å€ã¯1以äžn-1以äž
ã»ä»»æã®é£ç¶ãã2é
ã«ã€ããŠãa[i+1] > a[i]-2
ãšããæ¡ä»¶ãæºããæ°åãšäžå¯Ÿäžã«å¯Ÿå¿ãããšæããŸãã
ãããŠããã®ãããªæ°åã®åæ°ã¯ãæåŸã®é
ãäœãªã®ãã§åé¡ããŠæŒžååŒãäœãããšæããŸãã
No.2619DD++4æ25æ¥ 00:16
ãã¿ã ããã§çžŠç·ãnæ¬(nâ§3)ã§æšªç·ãkæ¬ã§ã®äœãæ¹Tn(k)ãæŒžååŒã§æ§æãããš
T3(k)=if(k==1,2,2*memorize(T3,k-1))
T4(k)=if(k==1,3,k==2,8,3*memorize(T4,k-1)-binomial(2,2)*memorize(T4,k-2))
T5(k)=if(k==1,4,k==2,13,4*memorize(T5,k-1)-binomial(3,2)*memorize(T5,k-2))
T6(k)=if(k==1,5,k==2,19,k==3,66,5*memorize(T6,k-1)-binomial(4,2)*memorize(T6,k-2)+binomial(3,3)*memorize(T6,k-3))
T7(k)=if(k==1,6,k==2,26,k==3,100,6*memorize(T7,k-1)-binomial(5,2)*memorize(T7,k-2)+binomial(4,3)*memorize(T7,k-3))
T8(k)=if(k==1,7,k==2,34,k==3,143,k==4,560,7*memorize(T8,k-1)-binomial(6,2)*memorize(T8,k-2)+binomial(5,3)*memorize(T8,k-3)-binomial(4,4)*memorize(T8,k-4))
T9(k)=if(k==1,8,k==2,43,k==3,196,k==4,820,8*memorize(T9,k-1)-binomial(7,2)*memorize(T9,k-2)+binomial(6,3)*memorize(T9,k-3)-binomial(5,4)*memorize(T9,k-4))
T10(k)=if(k==1,9,k==2,53,k==3,260,k==4,1156,k==5,4845,9*memorize(T10,k-1)-binomial(8,2)*memorize(T10,k-2)+binomial(7,3)*memorize(T10,k-3)-binomial(6,4)*memorize(T10,k-4)+binomial(5,5)*memorize(T10,k-5))
T11(k)=if(k==1,10,k==2,64,k==3,336,k==4,1581,k==5,6954,10*memorize(T11,k-1)-binomial(9,2)*memorize(T11,k-2)+binomial(8,3)*memorize(T11,k-3)-binomial(7,4)*memorize(T11,k-4)+binomial(6,5)*memorize(T11,k-5))
*ã¹ããŒãã¢ãããèšãããã¡ã¢åããŠåŠçããŠããŸãã
çžŠã®æ¬æ°ãå€ããªããšåæå€ãããã€ãéããªããšãããªãã®ã§ãã®èŸºãé¢åãïŒ
çžŠã®æ¬æ°
-3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11(æ¬)
æšªã®æ¬æ°;ã§èŠãŠäžããã
1;2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
2;4 | 8 | 13 | 19 | 26 | 34 | 43 | 53 | 64
3;8 | 21 | 40 | 66 | 100 | 143 | 196 | 260 | 336
4;16 | 55 | 121 | 221 | 364 | 560 | 820 | 1156 | 1581
5;32 | 144 | 364 | 728 | 1288 | 2108 | 3264 | 4845 | 6954
6;64 | 377 | 1093 | 2380 | 4488 | 7752 | 12597 | 19551 | 29260
7;128 | 987 | 3280 | 7753 | 15504 | 28101 | 47652 | 76912 | 119416
8;256 | 2584 | 9841 | 25213 | 53296 | 100947 | 177859 | 297275 | 476905
9;512 | 6765 | 29524 | 81927 | 182688 | 360526 | 657800 | 1134705 | 1874730
10;1024 | 17711 | 88573 | 266110 | 625184 | 1282735 | 2417416 | 4292145 | 7283640
11;2048 | 46368 | 265720 | 864201 | 2137408 | 4552624 | 8844448 | 16128061 | 28048800
12;4096 | 121393 | 797161 | 2806272 | 7303360 | 16131656 | 32256553 | 60304951 | 107286661
13;8192 | 317811 | 2391484 | 9112264 | 24946816 | 57099056 | 117378336 | 224660626 | 408239530
14;16384 | 832040 | 7174453 | 29587889 | 85196928 | 201962057 | 426440955 | 834641671 | 1547129284
15;32768 | 2178309 | 21523360 | 96072133 | 290926848 | 714012495 | 1547491404 | 3094322026 | 5844716616
16;65536 | 5702887 | 64570081 | 311945595 | 993379072 | 2523515514 | 5610955132 | 11453607152 | 22025185281
17;131072 | 14930352 | 193710244 | 1012883066 | 3391793664 | 8916942687 | 20332248992 | 42344301686 | 82836630954
18;262144 | 39088169 | 581130733 | 3288813893 | 11580678656 | 31504028992 | 73645557469 | 156404021389 | 311063682160
19;524288 | 102334155 | 1743392200 | 10678716664 | 39539651584 | 111295205284 | 266668876540 | 577291806894 | 1166646177136
20;1048576 | 267914296 | 5230176601 | 34673583028 | 134998297600 | 393151913464 | 965384509651 | 2129654436910 | 4371207361885
No.2620GAI4æ25æ¥ 15:48
ãŸã äœã®æ€èšŒãããŸããã... Python ã§ããã°ã©ã ããŠæ°ããååžããããªããŸããã
1282735ã¯ç·æ°ã®çã§ããçããã®æ°å€ãšåã£ãŠãªããããªæ°ãããŸã...
1282735
[764877, 279584, 133631, 64604, 27257, 9481, 2693, 608]
[279584, 478114, 262307, 147260, 72988, 29809, 9980, 2693]
[133631, 262307, 365985, 252938, 153368, 75216, 29809, 9481]
[64604, 147260, 252938, 314118, 250202, 153368, 72988, 27257]
[27257, 72988, 153368, 250202, 314118, 252938, 147260, 64604]
[9481, 29809, 75216, 153368, 252938, 365985, 262307, 133631]
[2693, 9980, 29809, 72988, 147260, 262307, 478114, 279584]
[608, 2693, 9481, 27257, 64604, 133631, 279584, 764877]
No.2621moonlight4æ26æ¥ 12:57
ãéšããããŸãããïŒç·šéã®ãã¹ã¯ãŒããééã£ãŠå
¥ããããã§èšæ£ã§ããªãã®ã§éããŠã®æçš¿ãšãªãç³ãèš³ãããŸããïŒ
Pythonã§çµãã ãã®ã¯ãªããªãåŠçãçµãããªãã®ã§
Claudiã«ãé¡ãããŠJuliaã«æžãçŽããŠè²°ã£ãŠå®è¡ãããšããããã®æéã§çµæãåºãŸããã
--start---------------------------------------
8 12
--Ans-------------------------------------------
16131656
[9188341, 3508269, 1778834, 939616, 451633, 184261, 63000, 17702]
[3508269, 5568480, 3238722, 1961381, 1086206, 507952, 197646, 63000]
[1778834, 3238722, 4168532, 3074842, 2048283, 1130230, 507952, 184261]
[939616, 1961381, 3074842, 3550353, 3019342, 2048283, 1086206, 451633]
[451633, 1086206, 2048283, 3019342, 3550353, 3074842, 1961381, 939616]
[184261, 507952, 1130230, 2048283, 3074842, 4168532, 3238722, 1778834]
[63000, 197646, 507952, 1086206, 1961381, 3238722, 5568480, 3508269]
[17702, 63000, 184261, 451633, 939616, 1778834, 3508269, 9188341]
--end-------------------------------------------
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No.2622moonlight4æ26æ¥ 15:11
GAI ãããž
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if k=1 then 2 else 2*T3(k-1) endif
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No.2623moonlight4æ26æ¥ 16:41
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No.2625moonlight4æ26æ¥ 17:06
çããã®å©ããåããŠå°ãåãçµãã ããšããŸãšããpdfãããã«çœ®ããŠãããŸãã
ãŸã 解決ããŠããŸããã®ã§ããå°ãå©ããŠäžããã
https://amaryllis4u.wordpress.com/2025/04/26/æšæºçãªããã¿ã ãããã§ããçãéžãã ãšãã«/
No.2626moonlight4æ26æ¥ 17:20
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Pythonã§å®è¡ããããã°AIã«ã§ã翻蚳ããŠããã£ãŠãã ããã
-----
#include <bits/stdc++.h>
using namespace std;
int main () {
int n, m;
cin >> n >> m;
assert(n>2);
vector<vector<vector<long long>>> a(n-1,vector<vector<long long>>(n,vector<long long>(n,0)));
for (int j=0; j<n; j++) {
a.at(0).at(j).at(j) = 1;
}
for (int loop=0; loop<m; loop++) {
vector<vector<vector<long long>>> next(n-1,vector<vector<long long>>(n,vector<long long>(n,0)));
for (int j=0; j<n; j++) {
for (int k=0; k<n; k++) {
next.at(0).at(j).at(k) = a.at(0).at(j).at(k) + a.at(1).at(j).at(k);
for (int i=1; i<n-2; i++) {
next.at(i).at(j).at(k) = next.at(i-1).at(j).at(k) + a.at(i+1).at(j).at(k);
}
next.at(n-2).at(j).at(k) = next.at(n-3).at(j).at(k);
}
}
for (int i=0; i<n-1; i++) {
for (int j=0; j<n; j++) {
swap (next.at(i).at(j).at(i),next.at(i).at(j).at(i+1));
}
}
swap (a,next);
}
long long total = 0LL;
for (int j=0; j<n; j++) {
for (int k=0; k<n; k++) {
long long sum = 0LL;
for (int i=0; i<n-1; i++) {
sum += a.at(i).at(j).at(k);
}
cout << sum;
if (k==n-1) {
total += sum;
cout << endl;
} else {
cout << " ";
}
}
}
cout << "total:" << total << endl;
return 0;
}
-----
åºåãµã³ãã«
8 12
9188341 3508269 1778834 939616 451633 184261 63000 17702
3508269 5568480 3238722 1961381 1086206 507952 197646 63000
1778834 3238722 4168532 3074842 2048283 1130230 507952 184261
939616 1961381 3074842 3550353 3019342 2048283 1086206 451633
451633 1086206 2048283 3019342 3550353 3074842 1961381 939616
184261 507952 1130230 2048283 3074842 4168532 3238722 1778834
63000 197646 507952 1086206 1961381 3238722 5568480 3508269
17702 63000 184261 451633 939616 1778834 3508269 9188341
total:16131656
5 30
69706010502882 64476946102498 61603155451959 58814544487309 54236041597325
64476946102498 62876755878626 61865352374327 60803099299213 58814544487309
61603155451959 61865352374327 61899682489401 61865352374327 61603155451959
58814544487309 60803099299213 61865352374327 62876755878626 64476946102498
54236041597325 58814544487309 61603155451959 64476946102498 69706010502882
total:308836698141973
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