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 A387623 #17 Sep 05 2025 12:27:12
%S A387623 1,1,1,1,3,13,31,57,95,193,463,1081,2295,4609,9423,20185,44071,94801,
%T A387623 199807,418921,885879,1889889,4034639,8573561,18155399,38461105,
%U A387623 81665695,173627401,368961431,783201921,1661811055,3527298329,7490519335,15908549329,33779968447
%N A387623 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k,2*k).
%H A387623 Vincenzo Librandi, <a href="/A387623/b387623.txt">Table of n, a(n) for n = 0..1500</a>
%H A387623 <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 A387623 G.f.: (1-x-2*x^4)/((1-x-2*x^4)^2 - 8*x^5).
%F A387623 a(n) = 2*a(n-1) - a(n-2) + 4*a(n-4) + 4*a(n-5) - 4*a(n-8).
%t A387623 Table[Sum[2^k*Binomial[2*n-6*k,2*k],{k,0,Floor[n/4]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 05 2025 *)
%o A387623 (PARI) a(n) = sum(k=0, n\4, 2^k*binomial(2*n-6*k, 2*k));
%o A387623 (Magma) [&+[2^k* Binomial(2*n-6*k, 2*k): k in [0..Floor (n/4)]]: n in [0..30]]; // _Vincenzo Librandi_, Sep 05 2025
%Y A387623 Cf. A001541, A108480, A387622.
%Y A387623 Cf. A387626, A387629.
%K A387623 nonn,easy,new
%O A387623 0,5
%A A387623 _Seiichi Manyama_, Sep 03 2025