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 A169637 The number of permutations of the first n elements of the Hofstaedter Q-sequence (A005185), augmented by Q(0)=1. 2
 1, 1, 1, 4, 20, 60, 420, 3360, 15120, 151200, 831600, 3326400, 43243200, 302702400, 1513512000, 24216192000, 411675264000, 3705077376000, 70396470144000, 703964701440000, 14783258730240000, 162615846032640000, 1246721486250240000, 7480328917501440000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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. LINKS Table of n, a(n) for n=0..23. Rémy Sigrist, PARI program for A169637 EXAMPLE 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). MATHEMATICA 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 *) PROG (PARI) See Links section. CROSSREFS Cf. A005185. Sequence in context: A135507 A197404 A355990 * A356012 A169638 A226424 Adjacent sequences: A169634 A169635 A169636 * A169638 A169639 A169640 KEYWORD nonn AUTHOR Roger L. Bagula, Apr 04 2010 EXTENSIONS Definition clarified, comment and example added - R. J. Mathar, Dec 08 2010 More terms from Rémy Sigrist, Jun 29 2021 STATUS approved

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Last modified May 30 14:00 EDT 2024. Contains 372968 sequences. (Running on oeis4.)