A101197 Lengths of successive words (starting with a) under the substitution: {a -> aab, b -> aac, c -> b}.

1, 3, 9, 25, 71, 199, 561, 1577, 4439, 12487, 35137, 98857, 278151, 782599, 2201937, 6195369, 17431351, 49044935, 137993185, 388258473, 1092406631, 3073602311, 8647907569, 24331808809, 68460135703, 192619882695

Offset: 0

Author

Jeroen F.J. Laros, Jan 22 2005

Keywords

• easy
• nonn

Examples

			a => aab => aabaabaac => aabaabaacaabaabaacaabaabb, thus a(0) = 1, a(1) = 3, a(2) = 9, a(3) = 25.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2, 3, -2).

Crossrefs

Cf. A101399, A101400.

Pairwise sums of A046672.

Programs

Maple

a:= n-> (<<0|1|0>, <0|0|1>, <-2|3|2>>^n. <<0, 1, 3>>)[2, 1]:
seq (a(n), n=0..30);  # Alois P. Heinz, May 06 2011

Mathematica

LinearRecurrence[{2,3,-2},{1,3,9},30] (* Harvey P. Dale, Jan 01 2019 *)

Formula

a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-3).

G.f.: -(x+1) / (-2*x^3+3*x^2+2*x-1).

Extensions

Terms >=1577 by Alois P. Heinz, May 06 2011