A298404 - OEIS

%I #4 Feb 10 2018 22:01:44

%S 1,1,1,2,4,9,18,36,67,125,223,397,687,1187,2013,3406,5692,9496,15711,

%T 25953,42633,69952,114348,186750,304235,495309,805055,1307888,2122480,

%U 3443311,5582140,9047492,14657365,23742086,38446176,62250698,100775021,163129819

%N a(n) = 2*a(n-1) - a(n-3) + a(ceiling(n/2)), where a(0) = 1, a(1) = 1, a(2) = 1.

%C a(n)/a(n-1) -> (1 + sqrt(5))/2, the golden ratio (A001622), so that (a(n)) has the growth rate of the Fibonacci numbers (A000045). See A298338 for a guide to related sequences.

%H Clark Kimberling, <a href="/A298404/b298404.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] - a[n - 3] + a[Ceiling[n/2]];

%t Table[a[n], {n, 0, 90}]  (* A298404  *)

%Y Cf. A001622, A000045, A298338, A298405.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Feb 10 2018