A176724 Triangle for number of partitions which define multiset repetition classes.

1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 0, 1, 0, 1, 2, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2, 1, 1, 1

Offset

1,42

Comments

For definitions, references, links and examples see the corresponding partition array A176723.

Row sums coincide with those of array A176723 for n>=1, and they are given by A007294.

If for n=0 a 1 is added (the empty partition defines the empty multiset class) the tabl structure will be lost.

Links

Table of n, a(n) for n=1..105.

W. Lang: First 15 rows and row sums.

Formula

a(n,m) is the number of m part partitions of n which define m-multiset repetition classes. Multiset repetition class defining is equivalent to the following constraint on the exponents of a partition (1^e[1],2^e[2],...,M^e[M]):

e[1] >= e[2]>=...>=e[M]>=1, i.e., positive nonincreasing with largest part M. This will satisfy T(M) <= n where T(M) = A000217(M) are the triangular numbers; for each n every sufficiently small positive M does occur.

Example

1;
0,1;
0,1,1;
0,0,1,1;
0,0,0,1,1;
0,0,1,1,1,1;
0,0,0,1,1,1,1;
...

Crossrefs

a(7,5)=1 because there is only one 5 part partition of 7 which is 5-multiset repetition class defining, namely (1^3,2^2) (see row n=7 of the partition array A176723). This defines the 5-multiset class representative {1,1,1,2,2}.

Sequence in context: A321929 A089198 A059607 * A015318 A026836 A089052

Adjacent sequences: A176721 A176722 A176723 * A176725 A176726 A176727

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Jul 14 2010

Extensions

Edited (in response to comments by Franklin T. Adams-Watters) by Wolfdieter Lang, Apr 02 2011

Status

approved