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A101197
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Lengths of successive words (starting with a) under the substitution: {a -> aab, b -> aac, c -> b}.
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1
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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; internal format)
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OFFSET
| 0,2
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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).
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EXAMPLE
| a => aab => aabaabaac => aabaabaacaabaabaacaabaabb, thus a(0) = 1, a(1) = 3, a(2) = 9, a(3) = 25.
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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
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CROSSREFS
| Cf. A101399, A101400.
Pairwise sums of A046672.
Sequence in context: A097861 A058719 A046661 * A101168 A079857 A101499
Adjacent sequences: A101194 A101195 A101196 * A101198 A101199 A101200
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KEYWORD
| easy,nonn
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AUTHOR
| J. F. J. Laros (jlaros(AT)liacs.nl), Jan 22 2005
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EXTENSIONS
| Terms >=1577 by Alois P. Heinz, May 6 2011.
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