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A299968 Number of normal generalized Young tableaux of size n with all rows and columns strictly increasing. 15
1, 1, 2, 5, 15, 51, 189, 753, 3248, 14738, 70658, 354178, 1857703, 10121033 (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..13.

D. E. Knuth, Permutations, matrices, and generalized Young tableaux, Pacific Journal of Mathematics, Vol. 34, No. 3 (1970), 709-727.

Wikipedia, Young tableau

EXAMPLE

The a(4) = 15 tableaux:

1 2 3 4

.

1 2 3   1 2 4   1 3 4   1 2 3   1 2 3

4       3       2       2       3

.

1 2   1 3   1 2

3 4   2 4   2 3

.

1 2   1 3   1 2   1 4   1 3

3     2     2     2     2

4     4     3     3     3

.

1

2

3

4

MATHEMATICA

unddis[y_]:=DeleteCases[y-#, 0]&/@Tuples[Table[If[y[[i]]>Append[y, 0][[i+1]], {0, 1}, {0}], {i, Length[y]}]];

dos[y_]:=With[{sam=Rest[unddis[y]]}, If[Length[sam]===0, If[Total[y]===0, {{}}, {}], Join@@Table[Prepend[#, y]&/@dos[sam[[k]]], {k, 1, Length[sam]}]]];

Table[Sum[Length[dos[y]], {y, IntegerPartitions[n]}], {n, 1, 8}]

CROSSREFS

Cf. A000085, A000898, A001221, A005117, A006958, A015128, A138178, A238690, A285175, A296561, A297388, A299926, A300120, A300122.

Sequence in context: A279554 A279555 A153197 * A279556 A108307 A275605

Adjacent sequences:  A299965 A299966 A299967 * A299969 A299970 A299971

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Feb 26 2018

STATUS

approved

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Last modified December 9 09:21 EST 2019. Contains 329877 sequences. (Running on oeis4.)