A169637 - OEIS

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

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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