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 A387511 #12 Sep 01 2025 16:59:52
%S A387511 1,2,4,14,64,248,868,3176,12352,48344,186688,720896,2810128,11021984,
%T A387511 43290688,170193632,670576384,2648370560,10477291072,41502538880,
%U A387511 164602863616,653632824704,2598446927872,10339935936512,41181966803200,164155849556480,654848284582912
%N A387511 a(n) = Sum_{k=0..floor(n/3)} 3^k * 2^(n-2*k) * binomial(n-2*k,k)^2.
%H A387511 Vincenzo Librandi, <a href="/A387511/b387511.txt">Table of n, a(n) for n = 0..1000</a>
%F A387511 G.f.: 1/sqrt((1-2*x-6*x^3)^2 - 48*x^4).
%t A387511 Table[Sum[3^k*2^(n-2*k)*Binomial[n-2*k,k]^2,{k,0,Floor[n/3]}],{n,0,30}] (* _Vincenzo Librandi_, Sep 01 2025 *)
%o A387511 (PARI) a(n) = sum(k=0, n\3, 3^k*2^(n-2*k)*binomial(n-2*k, k)^2);
%o A387511 (Magma) [(&+[3^k * 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 A387511 Cf. A108490.
%K A387511 nonn,new
%O A387511 0,2
%A A387511 _Seiichi Manyama_, Aug 31 2025