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 A387603 #17 Sep 03 2025 13:53:05
%S A387603 1,4,12,40,160,640,2416,8960,33664,127744,484096,1827840,6896896,
%T A387603 26049536,98440192,371939328,1404997632,5307301888,20049424384,
%U A387603 75742707712,286136467456,1080936235008,4083451559936,15426119532544,58275554459648,220148448624640,831657574400000
%N A387603 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 2^(n-k) * binomial(2*n-4*k+2,2*k+1).
%H A387603 Vincenzo Librandi, <a href="/A387603/b387603.txt">Table of n, a(n) for n = 0..1000</a>
%H A387603 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,8,16,0,-16).
%F A387603 G.f.: B(x)^2, where B(x) is the g.f. of A387509.
%F A387603 G.f.: 1/((1-2*x-4*x^3)^2 - 32*x^4).
%F A387603 a(n) = 4*a(n-1) - 4*a(n-2) + 8*a(n-3) + 16*a(n-4) - 16*a(n-6).
%t A387603 Table[Sum[2^(n-k)*Binomial[2*n-4*k+2, 2*k+1]/2,{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 03 2025 *)
%o A387603 (PARI) a(n) = sum(k=0, n\3, 2^(n-k)*binomial(2*n-4*k+2, 2*k+1))/2;
%o A387603 (Magma) [&+[2^(n-k)* Binomial(2*n-4*k+2, 2*k+1)/2: k in [0..Floor (n/3)]]: n in [0..35]]; // _Vincenzo Librandi_, Sep 03 2025
%Y A387603 Cf. A387509.
%K A387603 nonn,easy,new
%O A387603 0,2
%A A387603 _Seiichi Manyama_, Sep 02 2025