%I A112669
%S A112669 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,
%T A112669 54,72,108,36,6,9,84,102,172,117,15,0,1,3,84,174,306,228,54,7,3,18,
%U A112669 114,225,483,447,162,18,12,3,114,348,724,824,369,66,37,9,171,453
%N 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.
%C A112669 In other words, it shows how many partitions of n have k different partitions 
               of n+1 just covering it.
%e A112669 As an irregular triangle:
%e A112669 1
%e A112669 3
%e A112669 3 3
%e A112669 6 6 0 1
%e A112669 3 15 3 3
%e A112669 9 21 6 12
%e A112669 3 34 21 25 3
%e A112669 10 45 36 54 15
%e A112669 6 54 72 108 36 6
%e A112669 As a table:
%e A112669 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 A112669 n:=1 0 0 1 0 0 0 0 0 0 0 0 0
%e A112669 n:=2 0 0 3 0 0 0 0 0 0 0 0 0
%e A112669 n:=3 0 0 3 3 0 0 0 0 0 0 0 0
%e A112669 n:=4 0 0 6 6 0 1 0 0 0 0 0 0
%e A112669 n:=5 0 0 3 15 3 3 0 0 0 0 0 0
%e A112669 n:=6 0 0 9 21 6 12 0 0 0 0 0 0
%e A112669 n:=7 0 0 3 34 21 25 3 0 0 0 0 0
%e A112669 n:=8 0 0 10 45 36 54 15 0 0 0 0 0
%e A112669 n:=9 0 0 6 54 72 108 36 6 0 0 0 0
%Y A112669 Row sums are A000219; the weighted products (dot product with the k's) 
               is A090984.
%Y A112669 Sequence in context: A100049 A158315 A134059 this_sequence A098529 A133774 
               A108581
%Y A112669 Adjacent sequences: A112666 A112667 A112668 this_sequence A112670 A112671 
               A112672
%K A112669 nonn,tabf
%O A112669 1,2
%A A112669 Wouter Meeussen (wouter.meeussen(AT)pandora.be), Sep 07 2004