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 A387513 #13 Sep 01 2025 16:59:47
%S A387513 1,3,9,30,117,486,2034,8505,35721,151173,644274,2760237,11871846,
%T A387513 51223428,221624019,961221735,4177946385,18193784220,79361528679,
%U A387513 346693615128,1516579388406,6642203294691,29123170761807,127821123780795,561522735794574,2468882933230887
%N A387513 a(n) = Sum_{k=0..floor(n/3)} 3^(n-2*k) * binomial(n-2*k,k)^2.
%H A387513 Vincenzo Librandi, <a href="/A387513/b387513.txt">Table of n, a(n) for n = 0..1000</a>
%F A387513 G.f.: 1/sqrt((1-3*x-3*x^3)^2 - 36*x^4).
%t A387513 Table[Sum[3^(n-2*k)*Binomial[n-2*k,k]^2,{k,0,Floor[n/3]}],{n,0,30}] (* _Vincenzo Librandi_, Sep 01 2025 *)
%o A387513 (PARI) a(n) = sum(k=0, n\3, 3^(n-2*k)*binomial(n-2*k, k)^2);
%o A387513 (Magma) [(&+[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 A387513 Cf. A246840, A387510.
%K A387513 nonn,new
%O A387513 0,2
%A A387513 _Seiichi Manyama_, Aug 31 2025