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 A387553 #15 Sep 02 2025 14:12:22
%S A387553 1,0,4,8,12,80,80,448,976,2176,8256,14720,52416,124672,313600,956416,
%T A387553 2145536,6438912,16135168,42117120,117754880,290820096,812109824,
%U A387553 2091991040,5519691776,14911766528,38335299584,103777271808,271034662912,716987629568,1911288823808
%N A387553 a(n) = (1/2) * Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(2*k+2,2*n-4*k+1).
%H A387553 Vincenzo Librandi, <a href="/A387553/b387553.txt">Table of n, a(n) for n = 0..1500</a>
%H A387553 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,8,-4,16,-16).
%F A387553 G.f.: B(x)^2, where B(x) is the g.f. of A387483.
%F A387553 G.f.: 1/((1-2*x^2-4*x^3)^2 - 32*x^5).
%F A387553 a(n) = 4*a(n-2) + 8*a(n-3) - 4*a(n-4) + 16*a(n-5) - 16*a(n-6).
%t A387553 Table[Sum[2^(n-k)*Binomial[2*k+2, 2*n-4*k+1]/2,{k,0,Floor[n/2]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 02 2025 *)
%o A387553 (PARI) a(n) = sum(k=0, n\2, 2^(n-k)*binomial(2*k+2, 2*n-4*k+1))/2;
%o A387553 (Magma) [&+[2^(n-k) * Binomial(2*k+2, 2*n-4*k+1)/2: k in [0..Floor(n/2)]]: n in [0..40]]; // _Vincenzo Librandi_, Sep 02 2025
%Y A387553 Cf. A387483.
%K A387553 nonn,easy,new
%O A387553 0,3
%A A387553 _Seiichi Manyama_, Sep 02 2025