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A323582 Number of generalized Young tableaux with constant rows, weakly increasing columns, and entries summing to n. 3
1, 1, 3, 5, 11, 16, 33, 47, 85, 126, 208, 299, 486, 685, 1050, 1496, 2221, 3097, 4523, 6239, 8901 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For strictly increasing columns, see A100883.

LINKS

Table of n, a(n) for n=0..20.

EXAMPLE

The a(5) = 16 tableaux:

  5   11111

.

  1   2   11   111   111   1111

  4   3   3    2     11    1

.

  1   1   11   11   111

  1   2   1    11   1

  3   2   2    1    1

.

  1   11

  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.

Sequence in context: A074820 A327043 A006169 * A088328 A102643 A279767

Adjacent sequences:  A323579 A323580 A323581 * A323583 A323584 A323585

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jan 19 2019

STATUS

approved

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Last modified January 20 19:53 EST 2020. Contains 331096 sequences. (Running on oeis4.)