A298417 - OEIS

%I #4 Feb 11 2018 10:52:47

%S 1,1,1,5,13,37,105,289,801,2193,6025,16473,45101,123253,336997,920789,

%T 2516373,6875125,18785189,51322821,140222045,383095757,1046652077,

%U 2859512141,7812373537,21343816457,58312503241,159312762649,435250868777,1189127599849

%N a(n) = 2*a(n-1) + 2*a(n-2) + a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.

%C a(n)/a(n-1) -> 1+sqrt(3).

%H Clark Kimberling, <a href="/A298417/b298417.txt">Table of n, a(n) for n = 0..1000</a>

%t a[0] = 1; a[1] = 1; a[2] = 1;

%t a[n_] := a[n] = 2 a[n - 1] + 2 a[n - 2] + a[Floor[n/2]];

%t Table[a[n], {n, 0, 30}]  (* A298417 *)

%Y Cf. A298338, A298416.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Feb 11 2018