A298339 a(n) = a(n-1) + a(n-2) + a([n/2]), where a(0) = 1, a(1) = 2, a(2) = 3.

1, 2, 3, 7, 13, 23, 43, 73, 129, 215, 367, 605, 1015, 1663, 2751, 4487, 7367, 11983, 19565, 31763, 51695, 83825, 136125, 220555, 357695, 579265, 938623, 1519551, 2460925, 3983227, 6448639, 10436353, 16892359, 27336079, 44240421, 71588483, 115848469

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/2]];
Table[a[n], {n, 0, 30}]  (* A298339 *)