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 A094233 #18 Aug 28 2024 04:26:03
%S A094233 1,0,2,0,6,0,20,0,70,2,252,22,924,156,3432,910,12870,4760,48622,23256,
%T A094233 184796,108528,705894,490314,2708204,2163150,10430500,9373652,
%U A094233 40313160,40060078,156305070,169345560,607812102,709645552,2369918628,2952780320
%N A094233 Number of closed walks of length n at a vertex of the cyclic graph on 9 nodes C_9.
%C A094233 In general, a(n,m) = (2^n/m)*Sum_{k=0..m-1} cos(2*Pi*k/m)^n gives the number of closed walks of length n at a vertex of the cyclic graph on m nodes C_m.
%H A094233 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,-4,-5,2).
%F A094233 a(n) = (2^n/9)*Sum_{k=0..8} cos(2*Pi*k/9)^n.
%F A094233 G.f.: -(x-1)*(x^3+3*x^2-1)/((2*x-1)*(x+1)*(x^3-3*x^2+1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009
%F A094233 9*a(n) = 2*(-1)^n +2^n +6*(-1)^n*A188048(n). - _R. J. Mathar_, Nov 03 2020
%t A094233 f[n_] := FullSimplify[ TrigToExp[ 2^n/9 Sum[ Cos[2Pi*k/9]^n, {k, 0, 8}]]]; Table[ f[n], {n, 0, 40}] (* _Robert G. Wilson v_, Jun 01 2004 *)
%Y A094233 Cf. A078008, A054877, A047849.
%K A094233 nonn,easy
%O A094233 0,3
%A A094233 _Herbert Kociemba_, May 29 2004
%E A094233 More terms from _Robert G. Wilson v_, Jun 01 2004