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

Author

Wolfdieter Lang, Mar 14 2011

Keywords

• nonn
• tabf

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).

Examples

			[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}.
		

Links

• W. Lang: First 15 rows and corresponding multisets.

Crossrefs

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

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.

Extensions

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