OFFSET
0,4
COMMENTS
Number of ways to fill a (not necessarily square) matrix with the parts of an integer partition of n so that the rows and columns are strictly decreasing.
EXAMPLE
The a(8) = 12 matrices:
[8] [7 1] [6 2] [5 3] [5 2 1] [4 3 1]
.
[7] [6] [5] [3 2]
[1] [2] [3] [2 1]
.
[5] [4]
[2] [3]
[1] [1]
The a(10) = 22 matrices:
[10] [9 1] [8 2] [7 3] [7 2 1] [6 4] [6 3 1] [5 4 1] [5 3 2] [4 3 2 1]
.
[9] [8] [7] [6] [5 2] [4 2] [4 3]
[1] [2] [3] [4] [2 1] [3 1] [2 1]
.
[7] [6] [5] [5]
[2] [3] [4] [3]
[1] [1] [1] [2]
.
[4]
[3]
[2]
[1]
MATHEMATICA
Table[Sum[Length[Select[Union[Tuples[Select[IntegerPartitions[#, {k}], UnsameQ@@#&]&/@ptn]], And@@(OrderedQ[#, Greater]&/@Transpose[#])&]], {ptn, IntegerPartitions[n]}, {k, Min[ptn]}], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 15 2019
STATUS
approved