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 A387651 #17 Sep 05 2025 14:46:40
%S A387651 1,0,3,2,5,20,11,70,93,176,515,618,1877,3212,6043,14670,23469,55336,
%T A387651 104915,201202,442213,801924,1711787,3369814,6574205,13748896,
%U A387651 26354723,54064250,107762933,212616060,434126907,852642910,1721793229,3443972120,6839443699,13808517634
%N A387651 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(2*k+1,2*n-4*k+1).
%H A387651 Vincenzo Librandi, <a href="/A387651/b387651.txt">Table of n, a(n) for n = 0..1500</a>
%H A387651 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,4,-1,4,-4).
%F A387651 G.f.: (1+x^2-2*x^3)/((1+x^2-2*x^3)^2 - 4*x^2).
%F A387651 a(n) = 2*a(n-2) + 4*a(n-3) - a(n-4) + 4*a(n-5) - 4*a(n-6).
%t A387651 Table[Sum[2^(n-2*k)*Binomial[2*k+1,2*n-4*k+1],{k,0,Floor[n/2]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 05 2025 *)
%o A387651 (PARI) a(n) = sum(k=0, n\2, 2^(n-2*k)*binomial(2*k+1, 2*n-4*k+1));
%o A387651 (Magma) [&+[2^(n-2*k)* Binomial(2*k+1, 2*n-4*k+1): k in [0..Floor (n/2)]]: n in [0..40]]; // _Vincenzo Librandi_, Sep 05 2025
%Y A387651 Cf. A387627, A387652.
%Y A387651 Cf. A387647, A387649.
%K A387651 nonn,new
%O A387651 0,3
%A A387651 _Seiichi Manyama_, Sep 05 2025