

A300120


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


7



2, 6, 12, 26, 44, 86, 136, 239, 376, 613, 930, 1485, 2194, 3355, 4948, 7372, 10656, 15660, 22359, 32308
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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@@r1]}]]]]];
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: A034875 A136515 A141347 * A246584 A054454 A084170
Adjacent sequences: A300117 A300118 A300119 * A300121 A300122 A300123


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Feb 25 2018


STATUS

approved



