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A094052
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Number of walks of length n between two adjacent nodes in the cycle graph C_7.
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0
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0, 1, 0, 3, 0, 10, 1, 35, 9, 126, 55, 462, 286, 1717, 1365, 6451, 6188, 24463, 27132, 93518, 116281, 360031, 490337, 1394582, 2043275, 5430530, 8439210, 21242341, 34621041, 83411715, 141290436, 328589491, 574274008, 1297937234, 2326683921
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| In general a(n,m)=2^n/m*Sum_{k=0..m-1} Cos(2Pi*k/m)^(n+1) counts walks of length n between two adjacent nodes in the cycle graph C_m.
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FORMULA
| a(n)=2^n/7*Sum_{k=0..6} Cos(2Pi*k/7)^(n+1)
G.f.: x(1-x-x^2) / [(1-2x)(1+x-2x^2-x^3)].
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MATHEMATICA
| f[n_] := FullSimplify[ TrigToExp[ 2^n/7 Sum[ Cos[2Pi*k/7]^(n + 1), {k, 0, 6}]]]; Table[ f[n], {n, 0, 34}] (from Robert G. Wilson v Jun 01 2004)
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CROSSREFS
| Equals A095307(n+1) - A095308(n-1).
Sequence in context: A028850 A138364 A095364 * A161678 A081658 A119957
Adjacent sequences: A094049 A094050 A094051 * A094053 A094054 A094055
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KEYWORD
| easy,nonn
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AUTHOR
| Herbert Kociemba (kociemba(AT)t-online.de), May 31 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 01 2004
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