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 A300121 Number of normal generalized Young tableaux, of shape the integer partition with Heinz number n, with all rows and columns weakly increasing and all regions connected skew partitions. 38
 1, 1, 2, 2, 4, 5, 8, 4, 11, 12, 16, 12, 32, 28, 31, 8, 64, 31, 128, 33, 82, 64, 256, 28, 69, 144, 69, 86, 512, 105, 1024, 16, 208, 320, 209, 82, 2048, 704, 512, 86, 4096, 318, 8192, 216, 262, 1536, 16384, 64, 465, 262, 1232, 528, 32768, 209, 588, 245, 2912, 3328 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). LINKS EXAMPLE The a(9) = 11 tableaux: 1 1 1 1 . 2 1 1 1 1 1 1 2 1 1 1 2 2 2 1 2 . 1 1 1 2 1 2 1 3 2 3 1 3 3 3 2 3 . 1 2 1 3 3 4 2 4 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]]Table[PrimePi[p], {k}]]]]; Table[Length[cos[Reverse[primeMS[n]]]], {n, 50}] CROSSREFS Cf. A000085, A000898, A056239, A006958, A138178, A153452, A238690, A259479, A259480, A296150, A296561, A297388, A299699, A299925, A299926, A300056, A300060, A300118, A300120, A300122, A300123, A300124. Sequence in context: A319160 A292382 A296561 * A267046 A308902 A166515 Adjacent sequences: A300118 A300119 A300120 * A300122 A300123 A300124 KEYWORD nonn AUTHOR Gus Wiseman, Feb 25 2018 STATUS approved

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Last modified March 31 06:29 EDT 2023. Contains 361634 sequences. (Running on oeis4.)