A298403 a(n) = 2*a(n-1) - a(n-3) + a(floor(n/2)), where a(0) = 1, a(1) = 2, a(2) = 3.

1, 2, 3, 7, 15, 30, 60, 112, 209, 373, 664, 1149, 1985, 3366, 5695, 9517, 15877, 26268, 43392, 71280, 116956, 191184, 312237, 508667, 828135, 1346018, 2186735, 3548701, 5757079, 9333118, 15127052, 24506542, 39695843, 64280511, 104080748, 168491921, 272746723

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, A298402.

Programs

Mathematica

a[0] = 1; a[1] = 2; a[2] = 3;
a[n_] := a[n] = 2*a[n - 1] - a[n - 3] + a[Floor[n/2]];
Table[a[n], {n, 0, 90}]  (* A298403 *)