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A323582 Number of generalized Young tableaux with constant rows, weakly increasing columns, and entries summing to n. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
For strictly increasing columns, see A100883.
LINKS
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
Sequence in context: A074820 A327043 A006169 * A088328 A102643 A279767
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 19 2019
EXTENSIONS
a(21)-a(40) from Seiichi Manyama, Aug 20 2020
STATUS
approved

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)