A187447 Array for all multiset choices (multiset repetition class representatives in Abramowitz-Stegun order).

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 2, 3, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 3, 1, 1, 2, 3, 3, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 4, 3, 1, 1, 2, 3, 3, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 3, 1, 1, 3, 4, 4, 4, 3, 1, 1, 2, 3, 4, 3, 2, 1, 1, 2, 3, 3, 3, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 6, 4, 1, 1, 3, 5, 6, 5, 3, 1, 1, 3, 4, 4, 4, 4, 3, 1, 1, 2, 3, 4, 4, 3, 2, 1

Offset

0,8

Comments

The sequence of row lengths of this array is A187446(n)+1.

The considered multiset representatives are defined by certain partitions, taken in Abramowitz-Stegun (A-St)order. For this order see A036036, and for these partitions see A176723, as well as A176725 with a link.

This investigation was inspired by M. Griffiths and I. Mezo (see reference in A176725).

Links

Table of n, a(n) for n=0..185.

W. Lang: First 15 rows and corresponding multisets.

Formula

a(n,l), l=0,..,A187446(n), is the number "multiset choose l" for the multiset defined by the n-th multiset repetition class defining partition in A-St order.

a(n,0)=1, n>=0, by definition.

Example

[1],
[1, 1],
[1, 1, 1],
[1, 2, 1],
[1, 1, 1, 1],
[1, 2, 2, 1],
[1, 1, 1, 1, 1],
...
a(5,2)=2 because the 5th multiset repetition class defining partition in A-St order is 1^2,2 (a partition of N=4) which defines the 3-multiset {1,1,2}, and there are 2 possibilities to pick 2 elements from the multiset, namely 1,1 and 1,2.
a(6,4)=1 from picking all 4 elements from the 6th multiset representative in A-St order: {1,1,1,1}.

Crossrefs

Cf. A176723, A176724, A176725, A187445, A187446.

Sequence in context: A037830 A174353 A319582 * A146292 A139039 A279061

Adjacent sequences: A187444 A187445 A187446 * A187448 A187449 A187450

Keyword

nonn,tabf

Author

Wolfdieter Lang, Mar 14 2011

Extensions

Changed in response to a comment by Franklin T. Adams-Watters. - Wolfdieter Lang, Apr 02 2011

Status

approved