A308151 - OEIS

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A308151

Triangular array: each row partitions the partitions of n into n parts; of which the k-th part is the number of partitions having stay number k-1; see Comments.

1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 2, 3, 1, 0, 0, 1, 3, 3, 2, 2, 0, 0, 1, 4, 6, 2, 1, 1, 0, 0, 1, 5, 8, 4, 1, 2, 1, 0, 0, 1, 8, 10, 4, 4, 1, 1, 1, 0, 0, 1, 10, 14, 8, 3, 2, 2, 1, 1, 0, 0, 1, 13, 20, 9, 5, 3, 2, 1, 1, 1, 0, 0, 1, 18, 25, 12, 8, 5, 2

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,12

COMMENTS

The stay number of a partition P is defined as follows. Let U be the ordering of the parts of P in nonincreasing order, and let V be the reverse of U. The stay number of P is the number of numbers whose position in V is the same as in U. (1st column) = A238479. When the rows of the array are read in reverse order, it appears that the limiting sequence is A008483.

LINKS

Table of n, a(n) for n=1..84.

EXAMPLE

The first 8 rows:

0 1

0 1 1

1 1 0 1

1 2 1 0 1

2 3 1 0 0 1

3 3 2 2 0 0 1

4 6 2 1 1 0 0 1

5 8 4 1 2 1 0 0 1