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 A387552 #18 Sep 02 2025 14:12:41
%S A387552 1,0,0,4,4,0,12,40,12,32,224,224,112,960,2016,1152,3600,12672,13120,
%T A387552 15168,64256,110848,99904,291200,734912,836608,1376256,4114432,
%U A387552 6516224,8042496,20953088,43890688,56483072,107188224,260720640,404997120,609147904,1431527424
%N A387552 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 2^k * binomial(2*k+2,2*n-6*k+1).
%H A387552 Vincenzo Librandi, <a href="/A387552/b387552.txt">Table of n, a(n) for n = 0..1500</a>
%H A387552 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,4,4,0,-4,8,-4).
%F A387552 G.f.: B(x)^2, where B(x) is the g.f. of A387477.
%F A387552 G.f.: 1/((1-2*x^3-2*x^4)^2 - 16*x^7).
%F A387552 a(n) = 4*a(n-3) + 4*a(n-4) - 4*a(n-6) + 8*a(n-7) - 4*a(n-8).
%t A387552 Table[Sum[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 A387552 (PARI) a(n) = sum(k=0, n\3, 2^k*binomial(2*k+2, 2*n-6*k+1))/2;
%o A387552 (Magma) [&+[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 A387552 Cf. A387477.
%K A387552 nonn,easy,new
%O A387552 0,4
%A A387552 _Seiichi Manyama_, Sep 01 2025