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 A387629 #18 Sep 04 2025 10:54:14
%S A387629 1,3,5,7,11,31,83,183,351,675,1435,3231,7119,14987,30963,64871,138775,
%T A387629 298403,636091,1344191,2838399,6021371,12818467,27277207,57911207,
%U A387629 122790675,260485131,553185519,1175285967,2496108459,5298760307,11246985927,23877452663,50702334403
%N A387629 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k+1,2*k+1).
%H A387629 Vincenzo Librandi, <a href="/A387629/b387629.txt">Table of n, a(n) for n = 0..1000</a>
%H A387629 <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 A387629 G.f.: (1+x-2*x^4)/((1+x-2*x^4)^2 - 4*x).
%F A387629 a(n) = 2*a(n-1) - a(n-2) + 4*a(n-4) + 4*a(n-5) - 4*a(n-8).
%t A387629 Table[Sum[2^k*Binomial[2*n-6*k+1,2*k+1],{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 04 2025 *)
%o A387629 (PARI) a(n) = sum(k=0, n\4, 2^k*binomial(2*n-6*k+1, 2*k+1));
%o A387629 (Magma) [&+[2^k* Binomial(2*n-6*k+1, 2*k+1): k in [0..Floor (n/4)]]: n in [0..35]]; // _Vincenzo Librandi_, Sep 04 2025
%Y A387629 Cf. A001653, A387627, A387628.
%Y A387629 Cf. A387623, A387626.
%K A387629 nonn,easy,new
%O A387629 0,2
%A A387629 _Seiichi Manyama_, Sep 03 2025