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 A095368 #12 Dec 21 2024 17:47:43
%S A095368 1,0,5,1,21,8,84,45,330,221,1287,1015,5006,4488,19465,19380,75753,
%T A095368 82365,295261,346104,1152944,1442101,4510830,5969561,17682795,
%U A095368 24582663,69448446,100804436,273241161,411921832,1076832989
%N A095368 Number of walks of length n between two nodes at distance 3 in the cycle graph C_9.
%C A095368 In general (2^n/m)*Sum_{r=0..m-1} cos(2Pi*k*r/m)*cos(2Pi*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=3.
%H A095368 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,-4,-5,2).
%F A095368 a(n) = (2^n/9)*Sum_{r=0..8} cos(2Pi*r/3)*cos(2Pi*r/9)^n.
%F A095368 G.f.: (-1+x)x^3/((1+x)(-1+2x)(1-3x^2+x^3)).
%F A095368 a(n) = a(n-1)+5a(n-2)-4a(n-3)-5a(n-4)+2a(n-5).
%t A095368 LinearRecurrence[{1,5,-4,-5,2},{1,0,5,1,21},40] (* _Harvey P. Dale_, Dec 21 2024 *)
%Y A095368 Cf. A095364, A095367, A095369.
%K A095368 nonn,easy
%O A095368 3,3
%A A095368 _Herbert Kociemba_, Jul 03 2004