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A288925
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a(n) = a(n-1) + a(n-2) + 3*a(n-4) - 2*a(n-5) for n >= 5, where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 13, a(4) = 26.
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3
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2, 4, 8, 13, 26, 47, 89, 159, 300, 548, 1021, 1868, 3471, 6383, 11821, 21766, 40264, 74237, 137198, 253091, 467549, 862823, 1593492, 2941192, 5431149, 10025712, 18511691, 34173995, 63096749, 116485582, 215065980, 397050165, 733058402, 1353371815, 2498656993
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OFFSET
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0,1
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COMMENTS
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Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iterate of the mapping 00->1000, 10->0001, starting with 00; see A288226.
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-2) + 3*a(n-4) - 2*a(n-5) for n >= 5, where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 13, a(4) = 26.
G.f.: (1 + x)*(2 + 2*x^2 - x^3) / (1 - x - x^2 - 3*x^4 + 2*x^5). - Colin Barker, Jun 25 2017
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MATHEMATICA
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LinearRecurrence[{1, 1, 0, 3, -2}, {2, 4, 8, 13, 26}, 40]
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PROG
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(PARI) Vec((1 + x)*(2 + 2*x^2 - x^3) / (1 - x - x^2 - 3*x^4 + 2*x^5) + O(x^50)) \\ Colin Barker, Jun 25 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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