A298346 a(n) = a(n-1) + a(n-2) + 2 a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.

1, 1, 1, 4, 7, 13, 28, 49, 91, 154, 271, 451, 778, 1285, 2161, 3544, 5887, 9613, 15808, 25729, 42079, 68350, 111331, 180583, 293470, 475609, 771649, 1249828, 2025799, 3279949, 5312836, 8599873, 13924483, 22536130, 36479839, 59035195, 95546650, 154613461

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] + 2 a[Floor[n/2]];
Table[a[n], {n, 0, 30}]  (* A298346 *)