A298355 a(n) = a(n-1) + a(n-2) + 2 a([(n-1)/2]), where a(0) = 1, a(1) = 2, a(2) = 3.

1, 2, 3, 9, 16, 31, 53, 102, 173, 307, 512, 881, 1455, 2442, 4003, 6649, 10856, 17851, 29053, 47518, 77185, 125727, 203936, 331425, 537123, 871458, 1411491, 2287833, 3704208, 6000047, 9712261, 15725606, 25451165, 41198483, 66671360, 107905545, 174612607

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-1)/2]];
Table[a[n], {n, 0, 30}]  (* A298355 *)

Crossrefs

Cf. A001622, A000045, A298338.

Sequence in context: A092638 A206777 A173809 * A023147 A220123 A220125

Adjacent sequences: A298352 A298353 A298354 * A298356 A298357 A298358

Keyword

nonn,easy

Author

Clark Kimberling, Feb 10 2018

Status

approved