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A323431
Number of strict rectangular plane partitions of n.
6
1, 1, 1, 3, 3, 5, 7, 9, 11, 15, 21, 25, 33, 41, 53, 65, 81, 97, 121, 143, 173, 215, 255, 305, 367, 441, 527, 637, 751, 899, 1067, 1269, 1491, 1775, 2071, 2439, 2875, 3357, 3911, 4577, 5309, 6177, 7171, 8305, 9609, 11151
OFFSET
0,4
COMMENTS
Number of ways to fill a (not necessarily square) matrix with the parts of a strict integer partition of n so that the rows and columns are strictly decreasing.
EXAMPLE
The a(10) = 21 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] [4 2] [4 3]
[1] [2] [3] [4] [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[Sort/@Tuples[IntegerPartitions[#, {k}]&/@ptn]], UnsameQ@@Join@@#&&And@@OrderedQ/@Transpose[#]&]], {ptn, IntegerPartitions[n]}, {k, Min[ptn]}], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 16 2019
STATUS
approved