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 A387485 #13 Sep 01 2025 03:07:51
%S A387485 1,0,0,2,4,0,4,32,16,8,144,288,80,512,2304,2080,1856,12800,25664,
%T A387485 17408,58624,204928,242944,299520,1258752,2541568,2609152,6824448,
%U A387485 20169728,28344320,41747456,132358144,268472320,349177856,807964672,2116296704,3336458240
%N A387485 a(n) = Sum_{k=0..floor(n/3)} 2^(n-2*k) * binomial(k,n-3*k)^2.
%H A387485 Vincenzo Librandi, <a href="/A387485/b387485.txt">Table of n, a(n) for n = 0..2000</a>
%F A387485 G.f.: 1/sqrt((1-2*x^3-4*x^4)^2 - 32*x^7).
%t A387485 Table[Sum[2^(n-2*k)*Binomial[k,n-3*k]^2,{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 01 2025 *)
%o A387485 (PARI) a(n) = sum(k=0, n\3, 2^(n-2*k)*binomial(k, n-3*k)^2);
%o A387485 (Magma) [(&+[2^(n-2*k)* Binomial(k,n-3*k)^2: k in [0..Floor(n/3)]]): n in [0..40]]; // _Vincenzo Librandi_, Sep 01 2025
%Y A387485 Cf. A387483, A387484.
%K A387485 nonn,new
%O A387485 0,4
%A A387485 _Seiichi Manyama_, Aug 30 2025