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 A300122 Number of normal generalized Young tableaux of size n with all rows and columns weakly increasing and all regions connected skew partitions. 7
 1, 4, 13, 51, 183, 771, 3087, 13601, 59933, 278797, 1311719, 6453606, 32179898, 166075956, 871713213, 4704669005, 25831172649, 145260890323 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The diagram of a connected skew partition is required to be connected as a polyomino but can have empty rows or columns. 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(3) = 13 tableaux: 1 1 1   1 1 2   1 2 2   1 2 3 . 1 1   1 1   1 2   1 2   1 3 1     2     1     3     2 . 1   1   1   1 1   1   2   2 1   2   2   3 MATHEMATICA undcon[y_]:=Select[Tuples[Range[0, #]&/@y], Function[v, GreaterEqual@@v&&With[{r=Select[Range[Length[y]], y[[#]]=!=v[[#]]&]}, Or[Length[r]<=1, And@@Table[v[[i]]

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Last modified May 17 19:51 EDT 2022. Contains 353778 sequences. (Running on oeis4.)