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 A387624 #12 Sep 04 2025 05:26:47
%S A387624 1,1,7,21,63,213,671,2149,6911,22101,70847,227045,727391,2330901,
%T A387624 7468767,23931621,76683583,245713493,787329151,2522806629,8083720351,
%U A387624 25902323221,82997717407,265946059365,852159682431,2730539119701,8749350654527,28035173160421
%N A387624 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(2*n-2*k+1,2*k).
%H A387624 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,4,-4).
%F A387624 G.f.: (1-x+2*x^2)/((1-x+2*x^2)^2 - 8*x^2).
%F A387624 a(n) = 2*a(n-1) + 3*a(n-2) + 4*a(n-3) - 4*a(n-4).
%o A387624 (PARI) a(n) = sum(k=0, n\2, 2^k*binomial(2*n-2*k+1, 2*k));
%Y A387624 Cf. A002315, A387625, A387626.
%Y A387624 Cf. A387627.
%K A387624 nonn,easy,new
%O A387624 0,3
%A A387624 _Seiichi Manyama_, Sep 03 2025