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A101169
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Lengths of successive words (starting with a) under the substitution: {a -> aab, b -> aac, c -> ab}.
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0
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1, 3, 9, 26, 76, 221, 644, 1875, 5461, 15903, 46314, 134876, 392791, 1143896, 3331289, 9701475, 28252921, 82278978, 239615244, 697814501, 2032195756, 5918219771, 17235212309, 50192888175, 146173193506, 425689839228
(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) - a(n-3).
G.f.: -(x+1) / (-x^3+3*x^2+2*x-1).
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EXAMPLE
| a => aab => aabaabaac => aabaabaacaabaabaacaabaabab, thus a(0) = 1, a(1) = 3, a(2) = 9, a(3) = 26.
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MAPLE
| a:= n-> (<<0|1|0>, <0|0|1>, <-1|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.
Sequence in context: A123941 A018919 A005774 * A119826 A027915 A114982
Adjacent sequences: A101166 A101167 A101168 * A101170 A101171 A101172
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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 >=1875 by Alois P. Heinz, May 6 2011.
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