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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 8 00:00 EST 2023. Contains 360133 sequences. (Running on oeis4.)