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A101197 Lengths of successive words (starting with a) under the substitution: {a -> aab, b -> aac, c -> b}. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

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Last modified August 3 13:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)