A094052 Number of walks of length n between two adjacent nodes in the cycle graph C_7.
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
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (1, 4, -3, -2).
Programs
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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}] (* Robert G. Wilson v, Jun 01 2004 *)
Formula
a(n) = 2^n/7*Sum_{k=0..6} cos(2*Pi*k/7)^(n+1).
G.f.: x(1-x-x^2) / ((1-2x)(1+x-2x^2-x^3)).
7*a(n) = 2^n+A094648(n+1). - R. J. Mathar, Nov 05 2024
Extensions
More terms from Robert G. Wilson v, Jun 01 2004
Comments