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 A094659 #25 Aug 28 2024 05:00:50
%S A094659 1,0,2,0,6,0,20,2,70,18,252,110,924,572,3434,2730,12902,12376,48926,
%T A094659 54264,187036,232562,720062,980674,2789164,4086550,10861060,16878420,
%U A094659 42484682,69242082,166823430,282580872,657178982,1148548016,2595874468
%N A094659 Number of closed walks of length n at a vertex of the cyclic graph on 7 nodes C_7.
%C A094659 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 A094659 Harvey P. Dale, <a href="/A094659/b094659.txt">Table of n, a(n) for n = 0..1000</a>
%H A094659 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-3,-2).
%F A094659 a(n) = (2^n/7)*Sum_{k=0..6} cos(2*Pi*k/7)^n.
%F A094659 a(n) = 7(a(n-2) - 2a(n-4) + a(n-6)) + 2a(n-7).
%F A094659 G.f.: (1-x-2x^2+x^3)/((2x-1)(-1-x+2x^2+x^3)).
%F A094659 a(0)=1, a(1)=0, a(2)=2, a(3)=0, a(n)=a(n-1)+4*a(n-2)-3*a(n-3)-2*a(n-4). - _Harvey P. Dale_, Jun 12 2014
%F A094659 7*a(n) = 2^n + 2*A094648(n). - _R. J. Mathar_, Nov 03 2020
%t A094659 f[n_] := FullSimplify[ TrigToExp[ 2^n/7 Sum[Cos[2Pi*k/7]^n, {k, 0, 6}]]]; Table[ f[n], {n, 0, 36}] (* _Robert G. Wilson v_, Jun 09 2004 *)
%t A094659 LinearRecurrence[{1,4,-3,-2},{1,0,2,0},40] (* _Harvey P. Dale_, Jun 12 2014 *)
%Y A094659 Cf. A199572 (m=2), A078008 (m=3), A199573 (m=4), A054877 (m=5), A047849 (bisection of m=6), A063376 (bisection of m=8), A094233 (m=9), A095929 (bisection of m=10), A087433 (bisection of m=12).
%K A094659 nonn,easy
%O A094659 0,3
%A A094659 _Herbert Kociemba_, Jun 06 2004
%E A094659 More terms from _Robert G. Wilson v_, Jun 09 2004