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A187447 Array for all multiset choices (multiset repetition class representatives in Abramowitz-Stegun order). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 26 17:16 EDT 2022. Contains 354092 sequences. (Running on oeis4.)