A187446 Number of parts of the multiset repetition class defining partition (n,k) in Abramowitz-Stegun order.

0, 1, 2, 2, 3, 3, 4, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 5, 6, 6, 7, 8, 9, 4, 6, 7, 7, 8, 9, 10, 5, 7, 8, 8, 9, 10, 11, 6, 6, 7, 8, 8, 9, 9, 10, 11, 12, 6, 7, 7, 8, 9, 9, 10, 10, 11, 12, 13, 7, 8, 8, 9, 10, 10, 11, 11, 12

Offset

0,3

Comments

For the Abramowitz-Stegun (A-St) order of partitions see A036036.

For the first 87 multiset defining partitions in A-St order see a link under A176725.

This sequence is an irregular array with row length sequence A007294(n).

Links

Table of n, a(n) for n=0..70.

Formula

Sum(en[j],j=1..M(n)]), with the n-th multiset defining partition in A-St order written as (1^en[1],2^en[2],...,M^en[M]), with M=M(n) its largest part, and positive, nonincreasing exponents en[1]>=en[2]>=...>=en[M]>=1. a(0)=0 from the empty partition defining the empty multiset.

Example

Read as array:
0;
1;
2;
2,3;
3,4;
4,5;
3,4,5,6;
4,5,6,7;
5,6,7,8;
5,6,6,7,8,9;
4, 6, 7, 7, 8, 9, 10;
...,
linking (for row number n>=0) to the number of parts of the corresponding partitions of n.

Crossrefs

Cf. A176725, A187447.

Sequence in context: A080251 A220032 A219773 * A240020 A336430 A368086

Adjacent sequences: A187443 A187444 A187445 * A187447 A187448 A187449

Keyword

nonn,easy,tabf

Author

Wolfdieter Lang, Mar 14 2011

Status

approved