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 A387508 #13 Sep 02 2025 04:43:55
%S A387508 1,1,1,1,3,9,19,33,55,109,243,529,1071,2093,4179,8673,18255,37981,
%T A387508 77923,159649,329935,687117,1432403,2977505,6179215,12841597,26757059,
%U A387508 55840033,116551119,243209325,507658803,1060551137,2217515151,4639042909,9707403811
%N A387508 a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(n-3*k,k)^2.
%H A387508 Vincenzo Librandi, <a href="/A387508/b387508.txt">Table of n, a(n) for n = 0..1000</a>
%F A387508 G.f.: 1/sqrt((1-x-2*x^4)^2 - 8*x^5).
%t A387508 Table[Sum[2^k*Binomial[n-3*k, k]^2,{k,0,Floor[n/4]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 02 2025 *)
%o A387508 (PARI) a(n) = sum(k=0, n\4, 2^k*binomial(n-3*k, k)^2);
%o A387508 (Magma) [(&+[2^k * Binomial(n-3*k, k)^2: k in [0..Floor(n/4)]]): n in [0..40]]; // _Vincenzo Librandi_, Sep 02 2025
%Y A387508 Cf. A001850, A108488, A387507.
%Y A387508 Cf. A246883, A375293.
%K A387508 nonn,new
%O A387508 0,5
%A A387508 _Seiichi Manyama_, Aug 31 2025