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 A383583 #16 May 03 2025 14:22:14
%S A383583 1,0,0,0,1,0,0,2,3,0,3,12,10,4,30,60,40,60,210,286,231,560,1267,1428,
%T A383583 1722,4208,7182,8064,13275,28080,40656,51754,97020,176088,240251,
%U A383583 355872,667810,1081092,1506648,2475616,4401696,6693492,9904752,16950662,28359201
%N A383583 a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * binomial(k,n-3*k).
%H A383583 Vincenzo Librandi, <a href="/A383583/b383583.txt">Table of n, a(n) for n = 0..1000</a>
%F A383583 G.f.: (1/2) * ( 1 + 1/sqrt(1 - 4*x^4/(1-x^3)^2) ).
%F A383583 a(n) ~ phi^(n-1) / (2 * 5^(1/4) * sqrt(Pi*n)), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, May 01 2025
%t A383583 Table[Sum[Binomial[n-2*k-1,k]* Binomial[k,n-3*k],{k,0,Floor[n/3]}],{n,0,45}] (* _Vincenzo Librandi_, May 03 2025 *)
%o A383583 (PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(k, n-3*k));
%o A383583 (Magma) [&+[Binomial(n-2*k-1, k) * Binomial(k, n-3*k): k in [0..Floor(n div 3)]]: n in [0..45]]; // _Vincenzo Librandi_, May 03 2025
%Y A383583 Cf. A005717, A383584.
%Y A383583 Cf. A383571.
%K A383583 nonn
%O A383583 0,8
%A A383583 _Seiichi Manyama_, May 01 2025