This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A094052 #11 Nov 05 2024 06:26:40
%S A094052 0,1,0,3,0,10,1,35,9,126,55,462,286,1717,1365,6451,6188,24463,27132,
%T A094052 93518,116281,360031,490337,1394582,2043275,5430530,8439210,21242341,
%U A094052 34621041,83411715,141290436,328589491,574274008,1297937234,2326683921
%N A094052 Number of walks of length n between two adjacent nodes in the cycle graph C_7.
%C A094052 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 A094052 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 4, -3, -2).
%F A094052 a(n) = 2^n/7*Sum_{k=0..6} cos(2*Pi*k/7)^(n+1).
%F A094052 G.f.: x(1-x-x^2) / ((1-2x)(1+x-2x^2-x^3)).
%F A094052 7*a(n) = 2^n+A094648(n+1). - _R. J. Mathar_, Nov 05 2024
%t A094052 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 A094052 Equals A095307(n+1) - A095308(n-1).
%K A094052 easy,nonn
%O A094052 0,4
%A A094052 _Herbert Kociemba_, May 31 2004
%E A094052 More terms from _Robert G. Wilson v_, Jun 01 2004