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 A387601 #18 Sep 03 2025 12:32:34
%S A387601 1,2,3,4,9,26,63,128,241,486,1075,2412,5189,10770,22343,47352,101801,
%T A387601 218142,462635,976260,2065741,4391914,9351823,19877904,42164785,
%U A387601 89409718,189779059,403162268,856453269,1818474626,3859843799,8193466664,17396892537,36942391118
%N A387601 a(n) = (1/2) * Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k+2,2*k+1).
%H A387601 Vincenzo Librandi, <a href="/A387601/b387601.txt">Table of n, a(n) for n = 0..1000</a>
%H A387601 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,4,4,0,0,-4).
%F A387601 G.f.: B(x)^2, where B(x) is the g.f. of A387508.
%F A387601 G.f.: 1/((1-x-2*x^4)^2 - 8*x^5).
%F A387601 a(n) = 2*a(n-1) - a(n-2) + 4*a(n-4) + 4*a(n-5) - 4*a(n-8).
%t A387601 Table[Sum[2^k*Binomial[2*n-6*k+2, 2*k+1]/2,{k,0,Floor[n/4]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 03 2025 *)
%o A387601 (PARI) a(n) = sum(k=0, n\4, 2^k*binomial(2*n-6*k+2, 2*k+1))/2;
%o A387601 (Magma) [&+[2^k* Binomial(2*n-6*k+2, 2*k+1)/2: k in [0..Floor (n/4)]]: n in [0..35]]; // _Vincenzo Librandi_, Sep 03 2025
%Y A387601 Cf. A387508.
%K A387601 nonn,easy,new
%O A387601 0,2
%A A387601 _Seiichi Manyama_, Sep 02 2025