A298342 a(n) = a(n-1) + a(n-2) + a([2n/3]), where a(0) = 1, a(1) = 1, a(2) = 1.

1, 1, 1, 3, 5, 11, 21, 37, 69, 127, 217, 381, 667, 1117, 1911, 3245, 5373, 8999, 15039, 24705, 40861, 67477, 110249, 180971, 296593, 482937, 788529, 1286505, 2090073, 3401283, 5532217, 8974361, 14574055, 23658665, 38342969, 62182605, 100822167, 163301365

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[2n/3]];
Table[a[n], {n, 0, 30}]  (* A298342 *)