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 A095307 #15 Aug 29 2024 00:52:53
%S A095307 1,0,4,1,15,7,56,37,210,176,793,793,3017,3458,11561,14756,44592,62017,
%T A095307 172995,257775,674520,1062601,2641366,4352660,10381281,17742621,
%U A095307 40927033,72048354,161766061,291693136,640758252,1178135905,2542557383,4749439975,10103745288
%N A095307 Number of walks of length n between two nodes at distance 2 in the cycle graph C_7.
%C A095307 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=7 and k=2.
%H A095307 Colin Barker, <a href="/A095307/b095307.txt">Table of n, a(n) for n = 2..1000</a>
%H A095307 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-3,-2).
%F A095307 a(n) = (2^n/7)*Sum_{r=0..6} cos(4*Pi*r/7)*cos(2*Pi*r/7)^n.
%F A095307 a(n) = a(n-1) + 4*a(n-2) - 3*a(n-3) - 2*a(n-4).
%F A095307 G.f.: x^2*(1-x) / ((1-2*x)*(1+x-2*x^2-x^3)).
%t A095307 LinearRecurrence[{1,4,-3,-2},{1,0,4,1},40] (* _Harvey P. Dale_, Sep 22 2019 *)
%o A095307 (PARI) Vec(x^2*(1-x)/((1-2*x)*(1+x-2*x^2-x^3)) + O(x^40)) \\ _Colin Barker_, Nov 28 2015
%K A095307 nonn,easy
%O A095307 2,3
%A A095307 _Herbert Kociemba_, Jul 03 2004