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A112669
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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.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| In other words, it shows how many partitions of n have k different partitions of n+1 just covering it.
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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
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CROSSREFS
| Row sums are A000219; the weighted products (dot product with the k's) is A090984.
Sequence in context: A100049 A158315 A134059 * A098529 A133774 A108581
Adjacent sequences: A112666 A112667 A112668 * A112670 A112671 A112672
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KEYWORD
| nonn,tabf
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), Sep 07 2004
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