A136624 Irregular triangle read by rows: classify each numeric partition by sum of its parts and by the size of the staircase Ferrers board required to contain it. The triangle gives the number of partitions in each class, cf. A136102 and A136103.

1, 1, 2, 1, 2, 3, 3, 1, 2, 2, 6, 7, 6, 4, 1, 2, 2, 4, 8, 12, 15, 17, 14, 10, 5, 1

Offset

0,3

Comments

Sequences A136102 and A136103 encode the numeric partitions by least prime signature and the Ferrers boards by 1 2 12 360 75600 174636000 ... A006939. Note that the columns sum to 1 1 2 3 5 7 11 15 22 ... cf. A000041

Links

Table of n, a(n) for n=0..25.

Example

Starting a new row each time we are required to use a larger Ferrer board the triangle begins:
1
..1
.....2...1
.........2...3...3...1
.............2...2...6...7...6...4...1
.................2...2...4...8..12..15..17..14..10...5...1
.....................2...2...4
.........................2...2
.............................2

Crossrefs

Cf. A000041, A000108, A006939, A025487, A071724 (row sums), A136102, A136103.

Cf. A136625.

Sequence in context: A101933 A117127 A278148 * A033763 A033803 A035531

Adjacent sequences: A136621 A136622 A136623 * A136625 A136626 A136627

Keyword

more,nonn,tabf

Author

Alford Arnold, Jan 17 2008

Status

approved