A298405 a(n) = 2*a(n-1) - a(n-3) + a(ceiling(n/2)), where a(0) = 1, a(1) = 2, a(2) = 3.

1, 2, 3, 8, 17, 39, 78, 156, 290, 541, 965, 1718, 2973, 5137, 8712, 14741, 24635, 41099, 67998, 112326, 184518, 302756, 494904, 808263, 1316743, 2143719, 3484312, 5660593, 9186179, 14902787, 24159722, 39157900, 63437648, 102756673, 166396545, 269423440

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, A298404.

Programs

Mathematica

a[0] = 1; a[1] = 2; a[2] = 3;
a[n_] := a[n] = 2*a[n - 1] - a[n - 3] + a[Ceiling[n/2]];
Table[a[n], {n, 0, 90}]  (* A298405  *)