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 A387477 #13 Aug 31 2025 15:48:25
%S A387477 1,0,0,2,2,0,4,16,4,8,72,72,24,256,576,288,816,3200,3264,3104,14432,
%T A387477 25728,20672,58752,157120,173184,257152,809600,1296000,1466368,
%U A387477 3814400,8247296,10202368,18360320,46069760,71264768,100919808,238362624,457049088,635490304
%N A387477 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(k,n-3*k)^2.
%H A387477 Vincenzo Librandi, <a href="/A387477/b387477.txt">Table of n, a(n) for n = 0..2000</a>
%F A387477 G.f.: 1/sqrt((1-2*x^3-2*x^4)^2 - 16*x^7).
%t A387477 Table[Sum[2^k*Binomial[k,n-3*k]^2,{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Aug 31 2025 *)
%o A387477 (PARI) a(n) = sum(k=0, n\3, 2^k*binomial(k, n-3*k)^2);
%o A387477 (Magma) [(&+[2^k * Binomial(k,n-3*k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // _Vincenzo Librandi_, Aug 31 2025
%Y A387477 Cf. A375276, A387476.
%K A387477 nonn,new
%O A387477 0,4
%A A387477 _Seiichi Manyama_, Aug 30 2025