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 A095369 #16 Aug 29 2024 02:40:49
%S A095369 1,1,6,7,28,36,120,165,495,716,2003,3018,8024,12512,31977,51357,
%T A095369 127110,209475,504736,850840,2003784,3445885,7956715,13926276,
%U A095369 31609071,56191734,125640180,226444616,499685777,911607609,1988440598
%N A095369 Number of walks of length n between two nodes at distance 4 in the cycle graph C_9.
%C A095369 In general, (2^n/m)*Sum_{r=0..m-1} cos(2*Pi*k*r/m)*cos(2*Pi*r/m)^n is the number of walks of length n between two nodes at distance k in the cycle graph C_m. Here we have m=9 and k=4.
%H A095369 Michael De Vlieger, <a href="/A095369/b095369.txt">Table of n, a(n) for n = 4..3325</a>
%H A095369 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,-4,-5,2).
%F A095369 a(n) = (2^n/9)*Sum_{r=0..8} cos(8*Pi*r/9)*cos(2*Pi*r/9)^n.
%F A095369 G.f.: x^4/((1+x)(-1+2x)(1-3x^2+x^3)).
%F A095369 a(n) = a(n-1) + 5*a(n-2) - 4*a(n-3) - 5*a(n-4) + 2*a(n-5).
%t A095369 Drop[CoefficientList[Series[-x^4/((1 + x) (-1 + 2 x) (1 - 3 x^2 + x^3)), {x, 0, 34}], x], 4] (* _Michael De Vlieger_, Jan 23 2022 *)
%Y A095369 Cf. A095364, A095367, A095368.
%K A095369 nonn,easy
%O A095369 4,3
%A A095369 _Herbert Kociemba_, Jul 03 2004