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

0,4

Comments

In general, a(n,m) = 2^n/m*Sum_{k=0..m-1} cos(2*Pi*k/m)^(n+1) counts walks of length n between two adjacent nodes in the cycle graph C_m.

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (1, 4, -3, -2).

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

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 *)

Crossrefs

Equals A095307(n+1) - A095308(n-1).

Sequence in context: A028850 A138364 A095364 * A377573 A161678 A232267

Adjacent sequences: A094049 A094050 A094051 * A094053 A094054 A094055

Keyword

easy,nonn,changed

Author

Herbert Kociemba, May 31 2004

Extensions

More terms from Robert G. Wilson v, Jun 01 2004

Status

approved