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A169637
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The number of permutations of the first n elements of the Hofstaedter Q-sequence (A005185), augmented by Q(0)=1.
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1
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1, 1, 1, 4, 20, 60, 420, 3360, 15120, 151200, 831600, 3326400, 43243200
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OFFSET
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0,4
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COMMENTS
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An augmented Hofstadter sequence 1,1,1,2,3,3,... is defined by adding a single 1 in front of A005185. a(n) is the number of permutations using the first n+1 elements, 1 up to A005185(n), of this augmented sequence.
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LINKS
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Table of n, a(n) for n=0..12.
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EXAMPLE
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For n=3, the first 4 elements of the augmented sequence are (1,1,1,2), with a(3)=4 permutations, namely (1,1,1,2), (1,1,2,1), (1,2,1,1) and (2,1,1,1).
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MATHEMATICA
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f[0] = 1; f[1] = 1; f[2] = 1;
f[n_] := f[n] = f[n - f[n - 1]] + f[n - f[n - 2]];
a[m_] := Length[Permutations[Table[f[i], {i, 0, m}]]];
(* b = Table[a[m], {m, 0, 10}] *)
(* A much better way to compute the terms is to use the multinomials of the multiplicities of the terms of A005229! - Joerg Arndt, Dec 23 2014 *)
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CROSSREFS
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Cf. A005185.
Sequence in context: A018211 A135507 A197404 * A169638 A226424 A225260
Adjacent sequences: A169634 A169635 A169636 * A169638 A169639 A169640
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KEYWORD
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nonn,more
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AUTHOR
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Roger L. Bagula, Apr 04 2010
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EXTENSIONS
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Definition clarified, comment and example added - R. J. Mathar, Dec 08 2010
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STATUS
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approved
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