A323586 Number of plane partitions of n with no repeated rows (or, equivalently, no repeated columns).

1, 1, 2, 5, 8, 16, 30, 53, 89, 158, 265, 443, 735, 1197

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Example

The a(4) = 8 plane partitions with no repeated rows:
  4   31   22   211   1111
.
  3   21   111
  1   1    1
The a(6) = 30 plane partitions with no repeated columns:
  6   51   42   321
.
  5   4   41   3   31   32   31   22   21   221   211
  1   2   1    3   2    1    11   2    21   1     11
.
  4   3   31   2   21   22   21   111
  1   2   1    2   2    1    11   11
  1   1   1    2   1    1    1    1
.
  3   2   21   11
  1   2   1    11
  1   1   1    1
  1   1   1    1
.
  2   11
  1   1
  1   1
  1   1
  1   1
.
  1
  1
  1
  1
  1
  1

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
ptnplane[n_]:=Union[Map[Reverse@*primeMS, Join@@Permutations/@facs[n], {2}]];
Table[Sum[Length[Select[ptnplane[Times@@Prime/@y], And[UnsameQ@@#, And@@GreaterEqual@@@#, And@@(GreaterEqual@@@Transpose[PadRight[#]])]&]], {y, IntegerPartitions[n]}], {n, 10}]

Crossrefs

Cf. A000219, A003293 (strict rows), A114736 (strict rows and columns), A117433 (distinct entries), A299968, A319646 (no repeated rows or columns), A323429, A323436 (plane partitions of type), A323580, A323587.

Sequence in context: A026530 A336135 A032254 * A048237 A048139 A357239

Adjacent sequences: A323583 A323584 A323585 * A323587 A323588 A323589

Keyword

nonn,more

Author

Gus Wiseman, Jan 20 2019

Status

approved