A298353 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, 7, 12, 22, 37, 66, 110, 188, 310, 520, 852, 1409, 2298, 3773, 6137, 10020, 16267, 26475, 42930, 69715, 112955, 183190, 296665, 480707, 778224, 1260340, 2039973, 3302611, 5344882, 8651266, 13999921, 22657324, 36663382, 59330726, 96004128, 155351121

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}]  (* A298353 *)