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
Alois P. Heinz, Table of n, a(n) for n = 0..50 (first 46 terms from Ludovic Schwob)
D. E. Knuth, Permutations, matrices, and generalized Young tableaux, Pacific Journal of Mathematics, Vol. 34, No. 3 (1970), 709-727.
Wikipedia, Young tableau
FORMULA
a(n) = Sum_{k=0..n} 2^k * A238121(n,k). - Ludovic Schwob, Sep 23 2023
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 26 2018
EXTENSIONS
More terms from Ludovic Schwob, Sep 23 2023
STATUS
approved