A309098 Number of partitions of n avoiding the partition (4,3).

1, 1, 2, 3, 5, 7, 11, 14, 20, 25, 33, 39, 51, 58, 72, 82, 99, 110, 131, 143, 168, 183, 210, 226, 259, 277, 312, 333, 372, 394, 439, 462, 511, 537, 588, 617, 675, 705, 765, 798, 864, 898, 970, 1005, 1081, 1121, 1199, 1240, 1326, 1369, 1459, 1505, 1599, 1646

Offset

0,3

Comments

We say a partition alpha contains mu provided that one can delete rows and columns from (the Ferrers board of) alpha and then top/right justify to obtain mu. If this is not possible then we say alpha avoids mu. For example the only partitions avoiding (2,1) are those whose Ferrers boards are rectangles.

Links

Table of n, a(n) for n=0..53.

Jonathan Bloom, Nathan McNew, Counting pattern-avoiding integer partitions, arXiv:1908.03953 [math.CO], 2019.

J. Bloom and D. Saracino, On Criteria for rook equivalence of Ferrers boards, arXiv:1808.04221 [math.CO], 2018.

J. Bloom and D. Saracino, Rook and Wilf equivalence of integer partitions, arXiv:1808.04238 [math.CO], 2018.

J. Bloom and D. Saracino, Rook and Wilf equivalence of integer partitions, European J. Combin., 71 (2018), 246-267.

J. Bloom and D. Saracino, On Criteria for rook equivalence of Ferrers boards, European J. Combin., 76 (2018), 199-207.

Crossrefs

Cf. A309097, A309099, A309058.

Sequence in context: A325333 A036608 A309097 * A136185 A319471 A218506

Adjacent sequences: A309095 A309096 A309097 * A309099 A309100 A309101

Keyword

nonn

Author

Jonathan S. Bloom, Jul 12 2019

Extensions

More terms from Alois P. Heinz, Jul 12 2019

Status

approved