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 A387622 #14 Sep 05 2025 12:27:23
%S A387622 1,1,1,3,13,31,61,151,413,1031,2445,5991,15069,37447,91917,226503,
%T A387622 561373,1389735,3431501,8474983,20955229,51814407,128054029,316455559,
%U A387622 782209629,1933537511,4779082829,11812031271,29195752157,72164132167,178368130061
%N A387622 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*n-4*k,2*k).
%H A387622 Vincenzo Librandi, <a href="/A387622/b387622.txt">Table of n, a(n) for n = 0..1000</a>
%H A387622 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,4,4,0,-4).
%F A387622 G.f.: (1-x-2*x^3)/((1-x-2*x^3)^2 - 8*x^4).
%F A387622 a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3) + 4*a(n-4) - 4*a(n-6).
%t A387622 Table[Sum[2^k*Binomial[2*n-4*k,2*k],{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 05 2025 *)
%o A387622 (PARI) a(n) = sum(k=0, n\3, 2^k*binomial(2*n-4*k, 2*k));
%o A387622 (Magma) [&+[2^k* Binomial(2*n-4*k, 2*k): k in [0..Floor (n/3)]]: n in [0..30]]; // _Vincenzo Librandi_, Sep 05 2025
%Y A387622 Cf. A001541, A108480, A387623.
%K A387622 nonn,easy,new
%O A387622 0,4
%A A387622 _Seiichi Manyama_, Sep 03 2025