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A299967 Number of normal generalized Young tableaux of size n with all rows and columns weakly increasing and all regions non-singleton skew-partitions. 2
1, 0, 2, 3, 13, 32, 121, 376, 1406, 5030, 19632, 76334, 314582, 1308550, 5667494, 24940458, 113239394, 523149560, 2480434938, 11968944532, 59051754824 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 14 09:41 EST 2019. Contains 329979 sequences. (Running on oeis4.)