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 A387557 #16 Sep 02 2025 05:22:53
%S A387557 1,0,0,2,4,0,3,20,12,4,56,112,37,120,504,486,300,1584,3175,2124,4196,
%T A387557 13736,16576,14560,46217,92336,87024,145226,391124,540192,584267,
%U A387557 1397444,2742332,3162828,4973640,11517840,17306989,21377448,43440616,82902062,108691196
%N A387557 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 2^(n-3*k) * binomial(2*k+2,2*n-6*k+1).
%H A387557 Vincenzo Librandi, <a href="/A387557/b387557.txt">Table of n, a(n) for n = 0..2000</a>
%H A387557 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,4,0,-1,4,-4).
%F A387557 G.f.: B(x)^2, where B(x) is the g.f. of A387516.
%F A387557 G.f.: 1/((1-x^3-2*x^4)^2 - 8*x^7).
%F A387557 a(n) = 2*a(n-3) + 4*a(n-4) - a(n-6) + 4*a(n-7) - 4*a(n-8).
%t A387557 Table[Sum[2^(n-3*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 A387557 (PARI) a(n) = sum(k=0, n\3, 2^(n-3*k)*binomial(2*k+2, 2*n-6*k+1))/2;
%o A387557 (Magma) [&+[2^(n-3*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 A387557 Cf. A387516.
%K A387557 nonn,easy,new
%O A387557 0,4
%A A387557 _Seiichi Manyama_, Sep 02 2025