A300120 Number of skew partitions whose quotient diagram is connected and whose numerator has weight n.

2, 6, 12, 26, 44, 86, 136, 239, 376, 613, 930, 1485, 2194, 3355, 4948, 7372, 10656, 15660, 22359, 32308

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..20.

Example

The a(3) = 12 skew partitions:
(3)/()   (3)/(1)   (3)/(2)    (3)/(3)
(21)/()  (21)/(11) (21)/(2)   (21)/(21)
(111)/() (111)/(1) (111)/(11) (111)/(111)

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]]<y[[i+1]], {i, Range[Min@@r, Max@@r-1]}]]]]];
Table[Total[Length/@undcon/@IntegerPartitions[n]], {n, 10}]

Crossrefs

Cf. A000085, A000898, A006958, A138178, A238690, A259479, A259480, A297388, A299925, A299926, A300118, A300122, A300123, A300124.

Sequence in context: A136515 A141347 A335724 * A246584 A054454 A084170

Adjacent sequences: A300117 A300118 A300119 * A300121 A300122 A300123

Keyword

nonn,more

Author

Gus Wiseman, Feb 25 2018

Status

approved