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

0,2

Links

Table of n, a(n) for n=0..25.

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

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).

Example

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

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 *)

Crossrefs

Cf. A101399, A101400.

Pairwise sums of A046672.

Sequence in context: A058719 A046661 A309105 * A233828 A101168 A211287

Adjacent sequences: A101194 A101195 A101196 * A101198 A101199 A101200

Keyword

easy,nonn

Author

Jeroen F.J. Laros, Jan 22 2005

Extensions

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

Status

approved