cp's OEIS Frontend

A298344 a(n) = a(n-1) + a(n-2) + a([n/3]) + a([2n/3]), where a(0) = 1, a(1) = 1, a(2) = 1.

%I A298344 #4 Feb 09 2018 21:50:23
%S A298344 1,1,1,4,7,16,31,55,103,193,331,583,1024,1717,2941,5005,8293,13897,
%T A298344 23245,38197,63190,104383,170569,280012,458977,747385,1220362,1991185,
%U A298344 3234985,5264560,8563066,13891147,22558927,36621226,59351305,96253126,156064432
%N A298344 a(n) = a(n-1) + a(n-2) + a([n/3]) + a([2n/3]), where a(0) = 1, a(1) = 1, a(2) = 1.
%C A298344 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 A298344 Clark Kimberling, <a href="/A298344/b298344.txt">Table of n, a(n) for n = 0..1000</a>
%t A298344 a[0] = 1; a[1] = 1; a[2] = 1;
%t A298344 a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[n/3]] + a[Floor[2n/3]];
%t A298344 Table[a[n], {n, 0, 30}]  (* A298344 *)
%Y A298344 Cf. A001622, A000045, A298338.
%K A298344 nonn,easy
%O A298344 0,4
%A A298344 _Clark Kimberling_, Feb 09 2018