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 A387512 #13 Sep 02 2025 04:12:33
%S A387512 1,3,9,33,153,729,3357,15309,70713,331425,1565325,7418061,35250633,
%T A387512 168030369,803361645,3850647741,18495465561,88998869313,428955792525,
%U A387512 2070533412333,10007606103273,48428342800353,234607598151597,1137670448889501,5521881103615737
%N A387512 a(n) = Sum_{k=0..floor(n/3)} 2^k * 3^(n-2*k) * binomial(n-2*k,k)^2.
%H A387512 Vincenzo Librandi, <a href="/A387512/b387512.txt">Table of n, a(n) for n = 0..1000</a>
%F A387512 G.f.: 1/sqrt((1-3*x-6*x^3)^2 - 72*x^4).
%t A387512 Table[Sum[2^k*3^(n-2*k)*Binomial[n-2*k,k]^2,{k,0,Floor[n/3]}],{n,0,30}] (* _Vincenzo Librandi_, Sep 01 2025 *)
%o A387512 (PARI) a(n) = sum(k=0, n\3, 2^k*3^(n-2*k)*binomial(n-2*k, k)^2);
%o A387512 (Magma) [(&+[2^k * 3^(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 A387512 Cf. A387480.
%K A387512 nonn,new
%O A387512 0,2
%A A387512 _Seiichi Manyama_, Aug 31 2025