A298348 a(n) = a(n-1) + a(n-2) + a([(n+1)/2]), where a(0) = 1, a(1) = 1, a(2) = 1.

1, 1, 1, 3, 5, 11, 19, 35, 59, 105, 175, 299, 493, 827, 1355, 2241, 3655, 6001, 9761, 15937, 25873, 42109, 68281, 110883, 179657, 291367, 471851, 764573, 1237779, 2004593, 3244613, 5252861, 8501129, 13759991, 22267121, 36036873, 58313755, 94366565, 152696257

Offset: 0

Author

Clark Kimberling, Feb 10 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+1)/2]];
Table[a[n], {n, 0, 30}]  (* A298348 *)