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A187446
Number of parts of the multiset repetition class defining partition (n,k) in Abramowitz-Stegun order.
1
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).
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
Sequence in context: A080251 A220032 A219773 * A240020 A336430 A368086
KEYWORD
nonn,easy,tabf
AUTHOR
Wolfdieter Lang, Mar 14 2011
STATUS
approved