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 A383584 #16 May 02 2025 03:18:18
%S A383584 1,0,0,0,0,1,0,0,0,2,3,0,0,3,12,10,0,4,30,60,35,5,60,210,280,132,105,
%T A383584 560,1260,1267,630,1260,4200,6938,5796,4236,11550,27729,36396,28644,
%U A383584 34155,90100,168663,188100,163020,276573,631290,973830,995280,1068222,2111252,4104100
%N A383584 a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k-1,k) * binomial(k,n-4*k).
%H A383584 Vincenzo Librandi, <a href="/A383584/b383584.txt">Table of n, a(n) for n = 0..1000</a>
%F A383584 G.f.: (1/2) * ( 1 + 1/sqrt(1 - 4*x^5/(1-x^4)^2) ).
%t A383584 Table[Sum[Binomial[n-3*k-1,k]* Binomial[k,n-4*k],{k,0,Floor[n/4]}],{n,0,40}] (* _Vincenzo Librandi_, May 02 2025 *)
%o A383584 (PARI) a(n) = sum(k=0, n\4, binomial(n-3*k-1, k)*binomial(k, n-4*k));
%o A383584 (Magma) [&+[Binomial(n-3*k-1,k) * Binomial(k,n-4*k): k in [0..Floor(n div 4)]]: n in [0..45]]; // _Vincenzo Librandi_, May 02 2025
%Y A383584 Cf. A005717, A383583.
%Y A383584 Cf. A383572.
%K A383584 nonn
%O A383584 0,10
%A A383584 _Seiichi Manyama_, May 01 2025