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 A387507 #12 Sep 02 2025 05:23:49
%S A387507 1,1,1,3,9,19,37,87,217,507,1157,2727,6553,15627,37077,88519,212569,
%T A387507 510715,1226853,2952615,7120921,17192427,41538293,100458759,243211865,
%U A387507 589313755,1428931333,3467193191,8418640793,20453853003,49722339861,120936710471
%N A387507 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(n-2*k,k)^2.
%H A387507 Vincenzo Librandi, <a href="/A387507/b387507.txt">Table of n, a(n) for n = 0..1000</a>
%F A387507 G.f.: 1/sqrt((1-x-2*x^3)^2 - 8*x^4).
%t A387507 Table[Sum[2^k*Binomial[n-2*k, k]^2,{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 02 2025 *)
%o A387507 (PARI) a(n) = sum(k=0, n\3, 2^k*binomial(n-2*k, k)^2);
%o A387507 (Magma) [(&+[2^k * Binomial(n-2*k, k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // _Vincenzo Librandi_, Sep 02 2025
%Y A387507 Cf. A001850, A108488, A387508.
%Y A387507 Cf. A246840, A375292.
%K A387507 nonn,new
%O A387507 0,4
%A A387507 _Seiichi Manyama_, Aug 31 2025