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A323582
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Number of generalized Young tableaux with constant rows, weakly increasing columns, and entries summing to n.
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6
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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
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OFFSET
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0,3
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COMMENTS
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For strictly increasing columns, see A100883.
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LINKS
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EXAMPLE
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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
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1 1 1 1 1 1 1 1 1
1 2 1 1 1 1
3 2 2 1 1
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1 1 1
1 1
1 1
2 1
.
1
1
1
1
1
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A000085, A000219, A003293, A006951, A100883, A138178, A279784, A299968, A323432, A323436, A323437, A323438, A323450.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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