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 A095364 #18 Nov 14 2024 23:23:00 %S A095364 1,0,3,0,10,0,35,1,126,11,462,78,1716,455,6435,2380,24311,11628,92398, %T A095364 54264,352947,245157,1354102,1081575,5215250,4686826,20156580, %U A095364 20030039,78152535,84672780,303906051,354822776,1184959314,1476390160 %N A095364 Number of walks of length n between two adjacent nodes in the cycle graph C_9. %C A095364 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=1. %C A095364 Also, with offset 2, the cogrowth sequence of the 18-element group D9 = <S,T | S^9, T^2, (ST)^2>. - _Sean A. Irvine_, Nov 14 2024 %H A095364 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 5, -4, -5, 2). %F A095364 a(n) = 2^n/9 * sum(r=0..8, cos(2*Pi*r/9)^(n+1)). %F A095364 G.f.: x(-1+x+2x^2-x^3)/((1+x)(-1+2x)(1-3x^2+x^3)). %F A095364 a(n) = a(n-1) + 5*a(n-2) - 4*a(n-3) - 5*a(n-4) + 2*a(n-5). %o A095364 (PARI) a(n) = round(2^n/9*sum(r=0, 8, cos(2*Pi*r/9)^(n+1))) \\ _Michel Marcus_, Jul 18 2013 %o A095364 (PARI) Vec( x*(-1+x+2*x^2-x^3)/((1+x)*(-1+2*x)*(1-3*x^2+x^3))+O(x^66) ) \\ _Joerg Arndt_, Jul 18 2013 %Y A095364 Cf. A095367, A095368, A095369. %Y A095364 Cf. A007582 (D8), A377573 (D7). %K A095364 nonn %O A095364 1,3 %A A095364 _Herbert Kociemba_, Jul 03 2004