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A323586 Number of plane partitions of n with no repeated rows (or, equivalently, no repeated columns). 0
1, 1, 2, 5, 8, 16, 30, 53, 89, 158, 265, 443, 735, 1197 (list; graph; refs; listen; history; text; internal format)
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: A032233 A026530 A032254 * A048237 A048139 A071085

Adjacent sequences:  A323583 A323584 A323585 * A323587 A323588 A323589

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jan 20 2019

STATUS

approved

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Last modified December 12 20:12 EST 2019. Contains 329961 sequences. (Running on oeis4.)