OFFSET
1,2
COMMENTS
If y is an integer partition of n, 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.
EXAMPLE
The a(3) = 14 tableaux:
1 2 3 1 2 2 1 1 2 1 1 1
.
1 3 1 2 1 2 1 2 1 1 1 1
2 3 2 1 2 1
.
1 1 1 1
2 2 1 1
3 2 2 1
MATHEMATICA
undptns[y_]:=DeleteCases[Select[Tuples[Range[0, #]&/@y], OrderedQ[#, GreaterEqual]&], 0, {2}];
chn[y_]:=Join[{{{}, y}}, Join@@Function[c, Append[#, y]&/@chn[c]]/@Take[undptns[y], {2, -2}]];
Table[Sum[Length[chn[y]], {y, IntegerPartitions[n]}], {n, 8}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Feb 21 2018
STATUS
approved