A112669 Triangle read by rows: T(n,k) = number of plane partitions of n that can be extended in k ways to a plane partition of n+1 by adding 1 element to it.

1, 3, 3, 3, 6, 6, 0, 1, 3, 15, 3, 3, 9, 21, 6, 12, 3, 34, 21, 25, 3, 10, 45, 36, 54, 15, 6, 54, 72, 108, 36, 6, 9, 84, 102, 172, 117, 15, 0, 1, 3, 84, 174, 306, 228, 54, 7, 3, 18, 114, 225, 483, 447, 162, 18, 12, 3, 114, 348, 724, 824, 369, 66, 37, 9, 171, 453

Offset: 1

Author

Wouter Meeussen, Sep 07 2004

Keywords

• nonn
• tabf

Comments

In other words, it shows how many partitions of n have k different partitions of n+1 just covering it.

Examples

			As an irregular triangle:
1
3
3 3
6 6 0 1
3 15 3 3
9 21 6 12
3 34 21 25 3
10 45 36 54 15
6 54 72 108 36 6
As a table:
k:=1 k:=2 k:=3 k:=4 k:=5 k:=6 k:=7 k:=8 k:=9 k:=10 k:=11 k:=12
n:=1 0 0 1 0 0 0 0 0 0 0 0 0
n:=2 0 0 3 0 0 0 0 0 0 0 0 0
n:=3 0 0 3 3 0 0 0 0 0 0 0 0
n:=4 0 0 6 6 0 1 0 0 0 0 0 0
n:=5 0 0 3 15 3 3 0 0 0 0 0 0
n:=6 0 0 9 21 6 12 0 0 0 0 0 0
n:=7 0 0 3 34 21 25 3 0 0 0 0 0
n:=8 0 0 10 45 36 54 15 0 0 0 0 0
n:=9 0 0 6 54 72 108 36 6 0 0 0 0
		

Crossrefs

Row sums are A000219; the weighted products (dot product with the k's) is A090984.