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 A387509 #13 Sep 02 2025 04:12:25
%S A387509 1,2,4,12,48,176,592,2016,7168,25920,93440,336384,1216768,4425216,
%T A387509 16143360,58993664,215965696,792154112,2910720000,10710884352,
%U A387509 39464009728,145575002112,537583419392,1987177611264,7352243781632,27224715689984,100888181211136
%N A387509 a(n) = Sum_{k=0..floor(n/3)} 2^(n-k) * binomial(n-2*k,k)^2.
%H A387509 Vincenzo Librandi, <a href="/A387509/b387509.txt">Table of n, a(n) for n = 0..1000</a>
%F A387509 G.f.: 1/sqrt((1-2*x-4*x^3)^2 - 32*x^4).
%t A387509 Table[Sum[2^(n-k)*Binomial[n-2*k,k]^2,{k,0,Floor[n/3]}],{n,0,30}] (* _Vincenzo Librandi_, Sep 02 2025 *)
%o A387509 (PARI) a(n) = sum(k=0, n\3, 2^(n-k)*binomial(n-2*k, k)^2);
%o A387509 (Magma) [(&+[2^(n-k) * Binomial(n-2*k, k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // _Vincenzo Librandi_, Sep 02 2025
%Y A387509 Cf. A375276.
%K A387509 nonn,new
%O A387509 0,2
%A A387509 _Seiichi Manyama_, Aug 31 2025