A298354 a(n) = a(n-1) + a(n-2) + 2 a([(n-1)/2]), where a(0) = 1, a(1) = 1, a(2) = 1.

1, 1, 1, 4, 7, 13, 22, 43, 73, 130, 217, 373, 616, 1033, 1693, 2812, 4591, 7549, 12286, 20095, 32641, 53170, 86245, 140161, 227152, 368545, 596929, 967540, 1566535, 2537461, 4107382, 6650467, 10763473, 17423122, 28195777, 45633997, 73844872, 119503441

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] + 2 a[Floor[(n-1)/2]];
Table[a[n], {n, 0, 30}]  (* A298354 *)