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Search: id:A095933
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| A095933 |
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Number of walks of length 2n+1 between two nodes at distance 5 in the cycle graph C_10. |
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+0
1
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| 2, 14, 72, 330, 1430, 6008, 24786, 101118, 409640, 1652090, 6643782, 26667864, 106914242, 428292590, 1714834440, 6863694378, 27466183286, 109894593848, 439656551730, 1758830875230, 7035859329512, 28144840135514
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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In general Cos(2Pi*k*r/m)Cos(2Pi*r/m)^n is the number of walks of length n between two nodes at distance k in the cycle graph C_m. Here we have m=10 and k=5. Herbert
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FORMULA
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a(n)= 4^n/5*Sum_{r=0..9} (-1)^r*Cos(Pi*r/5)^(2n+1); a(n)=7a(n-1)-13a(n-2)+4a(n-3); G.f.: -2x^2/((-1+4x)(1-3x+x^2))
Recurrence: a(n)=7*a(n-1)-13*a(n-2)+4*a(n-3), where a(1)=2, a(2)=14, a(3)=72; formula a(n)=(8/5)*4^n+2/5*(sqrt(5)-2)*2^n*(3+sqrt(5))^(-n)-2/5*(sqrt(5)+2)*2^n*(3-sqrt(5))^(-n) - Maksym Voznyy (voznyy(AT)mail.ru), Jul 24 2008
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MATHEMATICA
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f[n_]:=FullSimplify[TrigToExp[(4^n/5)Sum[(-1)^k*Cos[Pi*k/5]^(2n+1), {k, 0, 9}]]]; Table[f[n], {n, 1, 35}]
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CROSSREFS
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Sequence in context: A072888 A094583 A002058 this_sequence A043011 A138156 A119913
Adjacent sequences: A095930 A095931 A095932 this_sequence A095934 A095935 A095936
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KEYWORD
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nonn
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AUTHOR
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Herbert Kociemba (kociemba(AT)t-online.de), Jul 12 2004
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