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 A387627 #16 Sep 04 2025 05:37:01
%S A387627 1,3,7,27,83,263,855,2723,8731,27999,89663,287355,920771,2950263,
%T A387627 9453607,30291667,97062123,311012623,996563855,3193247403,10231988371,
%U A387627 32785923879,105054547063,336621829635,1078623042491,3456186066623,11074510391007,35485583833307
%N A387627 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(2*n-2*k+1,2*k+1).
%H A387627 Vincenzo Librandi, <a href="/A387627/b387627.txt">Table of n, a(n) for n = 0..1000</a>
%H A387627 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,4,-4).
%F A387627 G.f.: (1+x-2*x^2)/((1+x-2*x^2)^2 - 4*x).
%F A387627 a(n) = 2*a(n-1) + 3*a(n-2) + 4*a(n-3) - 4*a(n-4).
%t A387627 Table[Sum[2^k*Binomial[2*n-2*k+1,2*k+1],{k,0,Floor[n/2]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 04 2025 *)
%o A387627 (PARI) a(n) = sum(k=0, n\2, 2^k*binomial(2*n-2*k+1, 2*k+1));
%o A387627 (Magma) [&+[2^k* Binomial(2*n-2*k+1, 2*k+1): k in [0..Floor (n/2)]]: n in [0..35]]; // _Vincenzo Librandi_, Sep 04 2025
%Y A387627 Cf. A001653, A387628, A387629.
%Y A387627 Cf. A099511.
%K A387627 nonn,easy,new
%O A387627 0,2
%A A387627 _Seiichi Manyama_, Sep 03 2025