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 A387600 #18 Sep 03 2025 12:32:26
%S A387600 1,2,3,8,25,62,139,340,877,2186,5311,13056,32497,80566,198595,490092,
%T A387600 1212597,2999522,7411207,18311384,45265657,111902478,276579275,
%U A387600 683566148,1689580733,4176276794,10322491919,25513684656,63061990401,155871106406,385266605779
%N A387600 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 2^k * binomial(2*n-4*k+2,2*k+1).
%H A387600 Vincenzo Librandi, <a href="/A387600/b387600.txt">Table of n, a(n) for n = 0..1500</a>
%H A387600 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,4,4,0,-4).
%F A387600 G.f.: B(x)^2, where B(x) is the g.f. of A387507.
%F A387600 G.f.: 1/((1-x-2*x^3)^2 - 8*x^4).
%F A387600 a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3) + 4*a(n-4) - 4*a(n-6).
%t A387600 Table[Sum[2^k*Binomial[2*n-4*k+2, 2*k+1]/2,{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 03 2025 *)
%o A387600 (PARI) a(n) = sum(k=0, n\3, 2^k*binomial(2*n-4*k+2, 2*k+1))/2;
%o A387600 (Magma) [&+[2^k* Binomial(2*n-4*k+2, 2*k+1)/2: k in [0..Floor (n/3)]]: n in [0..35]]; // _Vincenzo Librandi_, Sep 03 2025
%Y A387600 Cf. A387507.
%K A387600 nonn,easy,new
%O A387600 0,2
%A A387600 _Seiichi Manyama_, Sep 02 2025