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 A387510 #15 Sep 02 2025 04:12:16
%S A387510 1,2,4,10,32,104,324,1000,3136,9992,32064,103168,332816,1077152,
%T A387510 3497024,11381920,37121280,121285760,396922944,1300906112,4269367296,
%U A387510 14028169344,46143475712,151932559360,500710965504,1651533562368,5451595506688,18008220715520
%N A387510 a(n) = Sum_{k=0..floor(n/3)} 2^(n-2*k) * binomial(n-2*k,k)^2.
%H A387510 Vincenzo Librandi, <a href="/A387510/b387510.txt">Table of n, a(n) for n = 0..1000</a>
%F A387510 G.f.: 1/sqrt((1-2*x-2*x^3)^2 - 16*x^4).
%t A387510 Table[Sum[2^(n-2*k)*Binomial[n-2*k,k]^2,{k,0,Floor[n/3]}],{n,0,30}] (* _Vincenzo Librandi_, Sep 01 2025 *)
%o A387510 (PARI) a(n) = sum(k=0, n\3, 2^(n-2*k)*binomial(n-2*k, k)^2);
%o A387510 (Magma) [(&+[2^(n-2*k) * Binomial(n-2*k, k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // _Vincenzo Librandi_, Sep 01 2025
%Y A387510 Cf. A387507, A387509.
%Y A387510 Cf. A246840, A387513.
%K A387510 nonn,new
%O A387510 0,2
%A A387510 _Seiichi Manyama_, Aug 31 2025