|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|