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 A383582 #24 May 03 2025 09:40:48
%S A383582 1,2,6,20,71,256,942,3512,13221,50138,191260,733088,2821037,10892100,
%T A383582 42174848,163706656,636816019,2481902842,9689155902,37882580356,
%U A383582 148313102097,581365577564,2281393560802,8961689897248,35235582858441,138657185501870,546064549476476
%N A383582 a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * binomial(2*(n-4*k),n-4*k).
%H A383582 Vincenzo Librandi, <a href="/A383582/b383582.txt">Table of n, a(n) for n = 0..400</a>
%F A383582 G.f.: 1/sqrt((1 - x^4) * (1 - x^4 - 4*x)).
%F A383582 a(n) ~ (2 + sqrt(2) + sqrt(10 + 8*sqrt(2)))^n / (sqrt((sqrt(5 + 32*sqrt(2)) - 7)*Pi*n) * 2^(n + 7/4)). - _Vaclav Kotesovec_, May 01 2025
%t A383582 Table[Sum[Binomial[n-3*k,k]* Binomial[2*(n-4*k),n-4*k],{k,0,Floor[n/4]}],{n,0,30}] (* _Vincenzo Librandi_, May 02 2025 *)
%o A383582 (PARI) a(n) = sum(k=0, n\4, binomial(n-3*k, k)*binomial(2*(n-4*k), n-4*k));
%o A383582 (Magma) [&+[Binomial(n-3*k,k) * Binomial(2*(n-4*k),n-4*k): k in [0..n div 4]]: n in [0..45]]; // _Vincenzo Librandi_, May 02 2025
%Y A383582 Cf. A026375, A383573, A383581.
%Y A383582 Cf. A376792, A383572.
%Y A383582 Cf. A360292.
%K A383582 nonn
%O A383582 0,2
%A A383582 _Seiichi Manyama_, Apr 30 2025