A306320 Number of square plane partitions of n with distinct row sums and distinct column sums.

1, 1, 1, 1, 1, 2, 2, 5, 5, 10, 11, 18, 21, 31, 37, 56, 70, 97, 134, 180, 247, 343, 462, 623, 850, 1128, 1509, 2004, 2649, 3467, 4590, 5958, 7814, 10161, 13287, 17208, 22495, 29129, 37997, 49229, 64098, 82940, 107868, 139390, 180737, 233214, 301527, 388018, 500058

Offset

0,6

Links

Table of n, a(n) for n=0..48.

Example

The a(12) = 21 square plane partitions with distinct row sums and distinct column sums:
[twelve]
.
[64][73][82][91][54][63][72][81][44][53][53][62][62][71][43][43][52][52][61]
[11][11][11][11][21][21][21][21][31][22][31][22][31][31][32][41][32][41][41]
.
[221]
[211]
[111]

Mathematica

Table[Sum[Length[Select[Union[Reverse/@Sort/@Tuples[IntegerPartitions[#, {Length[ptn]}]&/@ptn]], UnsameQ@@Total/@#&&UnsameQ@@Total/@If[#=={}, {}, Transpose[#]]&&And@@OrderedQ/@Reverse/@If[#=={}, {}, Transpose[#]]&]], {ptn, IntegerPartitions[n]}], {n, 0, 20}]

Crossrefs

Cf. A000219, A089299 (square plane partitions), A101509, A271619, A279785, A306318, A323429, A323529, A323530, A323531.

Sequence in context: A214795 A287744 A214253 * A347449 A325347 A171967

Adjacent sequences: A306317 A306318 A306319 * A306321 A306322 A306323

Keyword

nonn

Author

Gus Wiseman, Feb 07 2019

Status

approved