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 A387626 #16 Sep 04 2025 10:53:50
%S A387626 1,1,1,1,7,21,43,73,131,297,715,1593,3259,6553,13723,29833,64827,
%T A387626 137881,289179,608329,1293083,2762457,5885179,12478601,26418363,
%U A387626 56028761,119072987,253139017,537620571,1140840793,2420927291,5139947401,10916332411,23182447833
%N A387626 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k+1,2*k).
%H A387626 Vincenzo Librandi, <a href="/A387626/b387626.txt">Table of n, a(n) for n = 0..1000</a>
%H A387626 <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 A387626 G.f.: (1-x+2*x^4)/((1-x+2*x^4)^2 - 8*x^4).
%F A387626 a(n) = 2*a(n-1) - a(n-2) + 4*a(n-4) + 4*a(n-5) - 4*a(n-8).
%t A387626 Table[Sum[2^k*Binomial[2*n-6*k+1,2*k],{k,0,Floor[n/4]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 04 2025 *)
%o A387626 (PARI) a(n) = sum(k=0, n\4, 2^k*binomial(2*n-6*k+1, 2*k));
%o A387626 (Magma) [&+[2^k* Binomial(2*n-6*k+1, 2*k): k in [0..Floor (n/4)]]: n in [0..35]]; // _Vincenzo Librandi_, Sep 04 2025
%Y A387626 Cf. A002315, A387624, A387625.
%K A387626 nonn,easy,new
%O A387626 0,5
%A A387626 _Seiichi Manyama_, Sep 03 2025