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 A387555 #17 Sep 02 2025 11:48:20
%S A387555 1,0,0,8,16,0,48,320,192,256,3584,7168,3328,30720,129024,129024,
%T A387555 245760,1622016,3272704,3293184,16596992,56360960,74776576,166985728,
%U A387555 752156672,1552941056,2268069888,8638693376,25806503936,41498443776,99265544192,357275009024
%N A387555 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 2^(n-k) * binomial(2*k+2,2*n-6*k+1).
%H A387555 Vincenzo Librandi, <a href="/A387555/b387555.txt">Table of n, a(n) for n = 0..1500</a>
%H A387555 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,8,16,0,-16,64,-64).
%F A387555 G.f.: B(x)^2, where B(x) is the g.f. of A387484.
%F A387555 G.f.: 1/((1-4*x^3-8*x^4)^2 - 128*x^7).
%F A387555 a(n) = 8*a(n-3) + 16*a(n-4) - 16*a(n-6) + 64*a(n-7) - 64*a(n-8).
%t A387555 Table[Sum[2^(n-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 A387555 (PARI) a(n) = sum(k=0, n\3, 2^(n-k)*binomial(2*k+2, 2*n-6*k+1))/2;
%o A387555 (Magma) [&+[2^(n-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 A387555 Cf. A387484.
%K A387555 nonn,easy,new
%O A387555 0,4
%A A387555 _Seiichi Manyama_, Sep 02 2025