A169637 The number of permutations of the first n elements of the Hofstaedter Q-sequence (A005185), augmented by Q(0)=1.

1, 1, 1, 4, 20, 60, 420, 3360, 15120, 151200, 831600, 3326400, 43243200, 302702400, 1513512000, 24216192000, 411675264000, 3705077376000, 70396470144000, 703964701440000, 14783258730240000, 162615846032640000, 1246721486250240000, 7480328917501440000

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