A298351 a(n) = a(n-1) + a(n-2) + 2 a(ceiling(n/2)), where a(0) = 1, a(1) = 2, a(2) = 3.

1, 2, 3, 11, 20, 53, 95, 188, 323, 617, 1046, 1853, 3089, 5318, 8783, 14747, 24176, 40157, 65567, 107816, 175475, 286997, 466178, 759353, 1231709, 2001698, 3244043, 5263307, 8524916, 13817717, 22372127, 36238196, 58658675, 94977185, 153716174, 248824493

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] = 2; a[2] = 3;
a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Ceiling[n/2]];
Table[a[n], {n, 0, 30}]  (* A298351 *)