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.

1, 1, 1, 4, 7, 16, 31, 55, 103, 193, 331, 583, 1024, 1717, 2941, 5005, 8293, 13897, 23245, 38197, 63190, 104383, 170569, 280012, 458977, 747385, 1220362, 1991185, 3234985, 5264560, 8563066, 13891147, 22558927, 36621226, 59351305, 96253126, 156064432

Offset: 0

Author

Clark Kimberling, Feb 09 2018

Keywords

• nonn
• easy

Comments

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.

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001622, A000045, A298338.

Programs

Mathematica

a[0] = 1; a[1] = 1; a[2] = 1;
a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[n/3]] + a[Floor[2n/3]];
Table[a[n], {n, 0, 30}]  (* A298344 *)