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 A371871 #11 Apr 22 2024 12:31:04
%S A371871 1,0,1,5,18,66,246,924,3493,13277,50697,194327,747319,2882061,
%T A371871 11142027,43167573,167561586,651513594,2537041938,9892847952,
%U A371871 38623197264,150959213886,590626854072,2312979822738,9065733950526,35561306875380,139595183125750
%N A371871 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k-2,n-3*k).
%F A371871 a(n) = [x^n] 1/((1-x^3) * (1-x)^(n-1)).
%F A371871 D-finite with recurrence 9*n*a(n) +3*(-17*n+16)*a(n-1) +3*(21*n-50)*a(n-2) +(-17*n+16)*a(n-3) +10*(2*n-5)*a(n-4)=0. - _R. J. Mathar_, Apr 22 2024
%p A371871 A371871 := proc(n)
%p A371871 1/(1-x^3)/(1-x)^(n-1) ;
%p A371871 coeftayl(%,x=0,n) ;
%p A371871 end proc:
%p A371871 seq(A371871(n),n=0..60) ; # _R. J. Mathar_, Apr 22 2024
%o A371871 (PARI) a(n) = sum(k=0, n\3, binomial(2*n-3*k-2, n-3*k));
%Y A371871 Cf. A360150, A371872, A371873.
%Y A371871 Cf. A105872, A371758.
%K A371871 nonn
%O A371871 0,4
%A A371871 _Seiichi Manyama_, Apr 10 2024