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 A387602 #19 Sep 03 2025 12:32:42
%S A387602 1,4,12,36,120,416,1420,4768,15968,53664,180736,608640,2048336,
%T A387602 6891968,23191104,78044352,262644608,883866624,2974400960,10009502720,
%U A387602 33684265984,113355412480,381467226112,1283724873728,4320028764416,14537889756160,48923344206848
%N A387602 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 2^(n-2*k) * binomial(2*n-4*k+2,2*k+1).
%H A387602 Vincenzo Librandi, <a href="/A387602/b387602.txt">Table of n, a(n) for n = 0..1500</a>
%H A387602 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,4,8,0,-4).
%F A387602 G.f.: B(x)^2, where B(x) is the g.f. of A387510.
%F A387602 G.f.: 1/((1-2*x-2*x^3)^2 - 16*x^4).
%F A387602 a(n) = 4*a(n-1) - 4*a(n-2) + 4*a(n-3) + 8*a(n-4) - 4*a(n-6).
%t A387602 Table[Sum[2^(n-2*k)*Binomial[2*n-4*k+2, 2*k+1]/2,{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 03 2025 *)
%o A387602 (PARI) a(n) = sum(k=0, n\3, 2^(n-2*k)*binomial(2*n-4*k+2, 2*k+1))/2;
%o A387602 (Magma) [&+[2^(n-2*k)* Binomial(2*n-4*k+2, 2*k+1)/2: k in [0..Floor (n/3)]]: n in [0..35]]; // _Vincenzo Librandi_, Sep 03 2025
%Y A387602 Cf. A375278, A387604.
%Y A387602 Cf. A387510.
%K A387602 nonn,easy,new
%O A387602 0,2
%A A387602 _Seiichi Manyama_, Sep 02 2025