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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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1
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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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
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a => aab => aabaabaac => aabaabaacaabaabaacaabaabab, thus a(0) = 1, a(1) = 3, a(2) = 9, a(3) = 26.
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MAPLE
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a:= n-> (<<0|1|0>, <0|0|1>, <-1|3|2>>^n. <<0, 1, 3>>)[2, 1]:
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MATHEMATICA
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LinearRecurrence[{2, 3, -1}, {1, 3, 9}, 40] (* Harvey P. Dale, Feb 19 2012 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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