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 A387647 #16 Sep 06 2025 15:49:38
%S A387647 1,0,1,2,1,12,5,30,61,64,281,314,857,1812,2701,7606,11925,26376,55393,
%T A387647 96402,223985,405276,835989,1726158,3233133,6901328,13260073,26731882,
%U A387647 54453001,105630628,217246237,427776358,856449221,1729791512,3411468145,6904065986
%N A387647 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(2*k,2*n-4*k).
%H A387647 Vincenzo Librandi, <a href="/A387647/b387647.txt">Table of n, a(n) for n = 0..1500</a>
%H A387647 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,4,-1,4,-4).
%F A387647 G.f.: (1-x^2-2*x^3)/((1-x^2-2*x^3)^2 - 8*x^5).
%F A387647 a(n) = 2*a(n-2) + 4*a(n-3) - a(n-4) + 4*a(n-5) - 4*a(n-6).
%t A387647 Table[Sum[2^(n-2*k)*Binomial[2*k,2*n-4*k],{k,0,Floor[n/2]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 06 2025 *)
%o A387647 (PARI) a(n) = sum(k=0, n\2, 2^(n-2*k)*binomial(2*k, 2*n-4*k));
%o A387647 (Magma) [&+[2^(n-2*k)* Binomial(2*k, 2*n-4*k): k in [0..Floor (n/2)]]: n in [0..40]]; // _Vincenzo Librandi_, Sep 06 2025
%Y A387647 Cf. A108480, A387648.
%K A387647 nonn,new
%O A387647 0,4
%A A387647 _Seiichi Manyama_, Sep 04 2025