A298349 a(n) = a(n-1) + a(n-2) + a([(n+1)/2]), where a(0) = 1, a(1) = 2, a(2) = 3.

1, 2, 3, 8, 14, 30, 52, 96, 162, 288, 480, 820, 1352, 2268, 3716, 6146, 10024, 16458, 26770, 43708, 70958, 115486, 187264, 304102, 492718, 799088, 1294074, 2096878, 3394668, 5497692, 8898506, 14406222, 23314752, 37737432, 61068642, 98832844, 159928256

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[Floor[(n+1)/2]];
Table[a[n], {n, 0, 30}]  (* A298349 *)