A298404 a(n) = 2*a(n-1) - a(n-3) + a(ceiling(n/2)), where a(0) = 1, a(1) = 1, a(2) = 1.

1, 1, 1, 2, 4, 9, 18, 36, 67, 125, 223, 397, 687, 1187, 2013, 3406, 5692, 9496, 15711, 25953, 42633, 69952, 114348, 186750, 304235, 495309, 805055, 1307888, 2122480, 3443311, 5582140, 9047492, 14657365, 23742086, 38446176, 62250698, 100775021, 163129819

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, A298405.

Programs

Mathematica

a[0] = 1; a[1] = 1; a[2] = 1;
a[n_] := a[n] = 2*a[n - 1] - a[n - 3] + a[Ceiling[n/2]];
Table[a[n], {n, 0, 90}]  (* A298404  *)