A112669 - OEIS

%I #2 Mar 30 2012 18:37:44

%S 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,

%T 72,108,36,6,9,84,102,172,117,15,0,1,3,84,174,306,228,54,7,3,18,114,

%U 225,483,447,162,18,12,3,114,348,724,824,369,66,37,9,171,453

%N 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.

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

%e As an irregular triangle:

%e 1

%e 3

%e 3 3

%e 6 6 0 1

%e 3 15 3 3

%e 9 21 6 12

%e 3 34 21 25 3

%e 10 45 36 54 15

%e 6 54 72 108 36 6

%e As a table:

%e k:=1 k:=2 k:=3 k:=4 k:=5 k:=6 k:=7 k:=8 k:=9 k:=10 k:=11 k:=12

%e n:=1 0 0 1 0 0 0 0 0 0 0 0 0

%e n:=2 0 0 3 0 0 0 0 0 0 0 0 0

%e n:=3 0 0 3 3 0 0 0 0 0 0 0 0

%e n:=4 0 0 6 6 0 1 0 0 0 0 0 0

%e n:=5 0 0 3 15 3 3 0 0 0 0 0 0

%e n:=6 0 0 9 21 6 12 0 0 0 0 0 0

%e n:=7 0 0 3 34 21 25 3 0 0 0 0 0

%e n:=8 0 0 10 45 36 54 15 0 0 0 0 0

%e n:=9 0 0 6 54 72 108 36 6 0 0 0 0

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

%K nonn,tabf

%O 1,2

%A _Wouter Meeussen_, Sep 07 2004