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

1,2

Comments

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

Links

Table of n, a(n) for n=1..67.

Example

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.

Sequence in context: A219217 A219686 A367761 * A098529 A133774 A108581

Adjacent sequences: A112666 A112667 A112668 * A112670 A112671 A112672

Keyword

nonn,tabf

Author

Wouter Meeussen, Sep 07 2004

Status

approved