A323582 Number of generalized Young tableaux with constant rows, weakly increasing columns, and entries summing to n.

1, 1, 3, 5, 11, 16, 33, 47, 85, 126, 208, 299, 486, 685, 1050, 1496, 2221, 3097, 4523, 6239, 8901, 12219, 17093, 23202, 32120, 43200, 58899, 78761, 106210, 140786, 188192, 247689, 327965, 429183, 563592, 732730, 955851, 1235370, 1600205, 2057743, 2649254

Offset

0,3

Comments

For strictly increasing columns, see A100883.

Links

Table of n, a(n) for n=0..40.

Example

The a(5) = 16 tableaux:
  5   1 1 1 1 1
.
  1   2    1 1   1 1 1   1 1 1   1 1 1 1
  4   3    3     2       1 1     1
.
  1   1    1 1   1 1     1 1 1
  1   2    1     1 1     1
  3   2    2     1       1
.
  1   1 1
  1   1
  1   1
  2   1
.
  1
  1
  1
  1
  1

Mathematica

comps[q_]:=Table[Table[Take[q, {Total[Take[c, i-1]]+1, Total[Take[c, i]]}], {i, Length[c]}], {c, Join@@Permutations/@IntegerPartitions[Length[q]]}];
Table[Sum[Length[Select[comps[ptn], And@@SameQ@@@#&&GreaterEqual@@Length/@#&]], {ptn, Sort/@IntegerPartitions[n]}], {n, 10}]

Crossrefs

Cf. A000085, A000219, A003293, A006951, A100883, A138178, A279784, A299968, A323432, A323436, A323437, A323438, A323450.

Sequence in context: A074820 A327043 A006169 * A088328 A102643 A279767

Adjacent sequences: A323579 A323580 A323581 * A323583 A323584 A323585

Keyword

nonn

Author

Gus Wiseman, Jan 19 2019

Extensions

a(21)-a(40) from Seiichi Manyama, Aug 20 2020

Status

approved