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 A387628 #15 Sep 04 2025 08:35:36
%S A387628 1,3,5,9,29,81,185,429,1093,2785,6817,16613,41181,102441,253049,
%T A387628 623693,1541557,3814929,9430545,23297397,57577997,142345721,351858985,
%U A387628 869614109,2149341925,5312698977,13131636417,32457015109,80223121469,198288112969,490110342873
%N A387628 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*n-4*k+1,2*k+1).
%H A387628 Vincenzo Librandi, <a href="/A387628/b387628.txt">Table of n, a(n) for n = 0..1000</a>
%H A387628 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,4,4,0,-4).
%F A387628 G.f.: (1+x-2*x^3)/((1+x-2*x^3)^2 - 4*x).
%F A387628 a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3) + 4*a(n-4) - 4*a(n-6).
%t A387628 Table[Sum[2^k*Binomial[2*n-4*k+1,2*k+1],{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 04 2025 *)
%o A387628 (PARI) a(n) = sum(k=0, n\3, 2^k*binomial(2*n-4*k+1, 2*k+1));
%o A387628 (Magma) [&+[2^k* Binomial(2*n-4*k+1, 2*k+1): k in [0..Floor (n/3)]]: n in [0..35]]; // _Vincenzo Librandi_, Sep 04 2025
%Y A387628 Cf. A001653, A387627, A387629.
%K A387628 nonn,easy,new
%O A387628 0,2
%A A387628 _Seiichi Manyama_, Sep 03 2025