A298345 a(n) = a(n-1) + a(n-2) + a([n/3]) + a([2n/3]), where a(0) = 1, a(1) = 2, a(2) = 3.

1, 2, 3, 10, 18, 40, 79, 140, 262, 491, 842, 1483, 2605, 4368, 7482, 12732, 21096, 35351, 59131, 97166, 160744, 265532, 433898, 712302, 1167558, 1901218, 3104389, 5065229, 8229240, 13392126, 21782952, 35336664, 57385990, 93158035, 150979406, 244851226

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] = 2; a[2] = 3;
a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[n/3]] + a[Floor[2n/3]];
Table[a[n], {n, 0, 30}]  (* A298345 *)