A298347 a(n) = a(n-1) + a(n-2) + 2 a([n/2]), where a(0) = 1, a(1) = 2, a(2) = 3.

1, 2, 3, 9, 18, 33, 69, 120, 225, 381, 672, 1119, 1929, 3186, 5355, 8781, 14586, 23817, 39165, 63744, 104253, 169341, 275832, 447411, 727101, 1178370, 1911843, 3096585, 5019138, 8126433, 13163133, 21307128, 34499433, 55835733, 90382800, 146266167, 236727297

Offset

0,2

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] = 2; a[2] = 3;
a[n_] := a[n] = a[n - 1] + a[n - 2] + 2 a[Floor[n/2]];
Table[a[n], {n, 0, 30}]  (* A298347 *)

Crossrefs

Cf. A001622, A000045, A298338.

Sequence in context: A065965 A296052 A108827 * A113201 A089753 A094679

Adjacent sequences: A298344 A298345 A298346 * A298348 A298349 A298350

Keyword

nonn,easy

Author

Clark Kimberling, Feb 10 2018

Status

approved