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 A099624 #9 Dec 16 2024 05:44:34
%S A099624 0,0,1,9,58,318,1591,7503,33976,149436,643261,2724357,11395654,
%T A099624 47210154,194121811,793526571,3228811492,13090123272,52917410041,
%U A099624 213437246145,859342367890,3455021317590,13875655896751,55677180731079
%N A099624 a(n) = Sum_{k=0..floor(n/2)} C(n-k,k+2)*3^(n-k-2)*(4/3)^k.
%C A099624 In general a(n) = Sum_{k=0..floor(n/2)} C(n-k,k+2)*u^(n-k-2)*(v/u)^k has g.f. x^2/((1-u*x)^2(1-u*x-v*x^2)) and satisfies the recurrence a(n) = 3u*a(n-1)-(3u^2-v)*a(n-2)+(u^3-2uv)*a(n-3)+u^2^v*a(n-4).
%H A099624 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9,-23,3,36).
%F A099624 G.f.: x^2/((1-3*x)^2*(1-3*x-4*x^2)).
%F A099624 a(n) = 9*a(n-1)-23*a(n-2)+3*a(n-3)+36*a(n-4).
%F A099624 a(n) = -(n/4+13/16)*3^n +(-1)^n/80 +4^(n+1)/5 . - _R. J. Mathar_, Dec 16 2024
%Y A099624 Cf. A099623.
%K A099624 easy,nonn
%O A099624 0,4
%A A099624 _Paul Barry_, Oct 25 2004