A299967 Number of normal generalized Young tableaux of size n with all rows and columns weakly increasing and all regions non-singleton skew-partitions.

1, 0, 2, 3, 13, 32, 121, 376, 1406, 5030, 19632, 76334, 314582, 1308550, 5667494, 24940458, 113239394, 523149560, 2480434938, 11968944532, 59051754824

Offset

0,3

Comments

A generalized Young tableau of shape y is an array obtained by replacing the dots in the Ferrers diagram of y with positive integers. A tableau is normal if its entries span an initial interval of positive integers.

Links

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

Example

The a(4) = 13 tableaux:
1 1 2 2   1 1 1 1
.
1 2 2   1 1 2   1 1 1
1       2       1
.
1 2   1 1   1 1
1 2   2 2   1 1
.
1 2  1 1   1 1
1    2     1
2    2     1
.
1   1
1   1
2   1
2   1

Mathematica

undptns[y_]:=DeleteCases[Select[Tuples[Range[0, #]&/@y], OrderedQ[#, GreaterEqual]&], 0, {2}];
ehn[y_]:=ehn[y]=If[Total[y]=!=1, 1, 0]+Sum[ehn[c], {c, Select[undptns[y], Total[#]>1&&Total[y]-Total[#]>1&]}];
Table[Sum[ehn[y], {y, IntegerPartitions[n]}], {n, 15}]

Crossrefs

Cf. A000085, A063834, A138178, A153452, A238690, A296188, A297388, A299925, A299926, A299966.

Sequence in context: A072997 A037428 A073688 * A216359 A169983 A151461

Adjacent sequences: A299964 A299965 A299966 * A299968 A299969 A299970

Keyword

nonn,more

Author

Gus Wiseman, Feb 22 2018

Status

approved