A094052 - OEIS

%I #11 Nov 05 2024 06:26:40

%S 0,1,0,3,0,10,1,35,9,126,55,462,286,1717,1365,6451,6188,24463,27132,

%T 93518,116281,360031,490337,1394582,2043275,5430530,8439210,21242341,

%U 34621041,83411715,141290436,328589491,574274008,1297937234,2326683921

%N Number of walks of length n between two adjacent nodes in the cycle graph C_7.

%C 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.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 4, -3, -2).

%F a(n) = 2^n/7*Sum_{k=0..6} cos(2*Pi*k/7)^(n+1).

%F G.f.: x(1-x-x^2) / ((1-2x)(1+x-2x^2-x^3)).

%F 7*a(n) = 2^n+A094648(n+1). - _R. J. Mathar_, Nov 05 2024

%t 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 *)

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

%K easy,nonn

%O 0,4

%A _Herbert Kociemba_, May 31 2004

%E More terms from _Robert G. Wilson v_, Jun 01 2004