|
| |
|
|
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: A018211 A135507 A197404 * A169638 A226424 A225260
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
|
| |
|
|
