A300118 Number of skew partitions whose quotient diagram is connected and whose numerator is the integer partition with Heinz number n.

1, 2, 3, 3, 4, 4, 5, 4, 6, 5, 6, 5, 7, 6, 7, 5, 8, 7, 9, 6, 8, 7, 10, 6, 10, 8, 10, 7, 11, 8, 12, 6, 9, 9, 11, 8, 13, 10, 10, 7, 14, 9, 15, 8, 11, 11, 16, 7, 15, 11, 11, 9, 17, 11, 12, 8, 12, 12, 18, 9, 19, 13, 12, 7, 13, 10, 20, 10, 13, 12, 21, 9, 22, 14, 15, 11

Offset: 1

Author

Gus Wiseman, Feb 25 2018

Keywords

• nonn

Comments

The diagram of a connected skew partition is required to be connected as a polyomino but can have empty rows or columns.

Examples

			The a(15) = 7 denominators are (), (1), (11), (22), (3), (31), (32) with diagrams:
o o o   . o o   . o o   . . o   . . .   . . .   o o o
o o     o o     . o     . .     o o     . o     o o
Missing are the two disconnected skew partitions:
. . o   . . o
o o     . o
		

Crossrefs

Cf. A000085, A000898, A056239, A006958, A138178, A153452, A238690, A259479, A259480, A296150, A297388, A299925, A299926, A300056, A300060, A300120, A300122, A300123, A300124.

Programs

Mathematica

primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
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]]