A298402 a(n) = 2*a(n-1) - a(n-3) + a(floor(n/2)), where a(0) = 1, a(1) = 1, a(2) = 1.

1, 1, 1, 2, 4, 8, 16, 30, 56, 100, 178, 308, 532, 902, 1526, 2550, 4254, 7038, 11626, 19098, 31336, 51224, 83658, 136288, 221884, 360642, 585898, 950814, 1542512, 2500652, 4053040, 6566118, 10635838, 17222890, 27886700, 45144600, 73077936, 118280798

Offset

0,4

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

Mathematica

a[0] = 1; a[1] = 1; a[2] = 1;
a[n_] := a[n] = 2*a[n - 1] - a[n - 3] + a[Floor[n/2]];
Table[a[n], {n, 0, 90}]  (* A298402 *)

Crossrefs

Cf. A001622, A000045, A298338, A298403.

Sequence in context: A347775 A075529 A005305 * A125548 A227298 A164229

Adjacent sequences: A298399 A298400 A298401 * A298403 A298404 A298405

Keyword

nonn,easy

Author

Clark Kimberling, Feb 10 2018

Status

approved