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 A387556 #16 Sep 02 2025 09:27:12
%S A387556 1,0,0,4,8,0,12,80,48,32,448,896,336,1920,8064,7872,8320,50688,101824,
%T A387556 79616,262400,879616,1096704,1490944,5888256,11923456,13332480,
%U A387556 34886656,100288512,146227200,228961280,702910464,1430450176,1968660480,4587044864
%N A387556 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 2^(n-2*k) * binomial(2*k+2,2*n-6*k+1).
%H A387556 Vincenzo Librandi, <a href="/A387556/b387556.txt">Table of n, a(n) for n = 0..1500</a>
%H A387556 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,4,8,0,-4,16,-16).
%F A387556 G.f.: B(x)^2, where B(x) is the g.f. of A387485.
%F A387556 G.f.: 1/((1-2*x^3-4*x^4)^2 - 32*x^7).
%F A387556 a(n) = 4*a(n-3) + 8*a(n-4) - 4*a(n-6) + 16*a(n-7) - 16*a(n-8).
%t A387556 Table[Sum[2^(n-2*k)*Binomial[2*k+2, 2*n-6*k+1]/2,{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 02 2025 *)
%o A387556 (PARI) a(n) = sum(k=0, n\3, 2^(n-2*k)*binomial(2*k+2, 2*n-6*k+1))/2;
%o A387556 (Magma) [&+[2^(n-2*k) * Binomial(2*k+2, 2*n-6*k+1)/2: k in [0..Floor(n/3)]]: n in [0..40]]; // _Vincenzo Librandi_, Sep 02 2025
%Y A387556 Cf. A387485.
%K A387556 nonn,easy,new
%O A387556 0,4
%A A387556 _Seiichi Manyama_, Sep 02 2025