A309194 Number of partitions of n avoiding the partition (4,3,2).

1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 51, 67, 82, 105, 125, 154, 180, 218, 250, 295, 334, 390, 436, 502, 553, 630, 694, 780, 849, 950, 1027, 1138, 1230, 1355, 1447, 1590, 1694, 1846, 1971, 2133, 2257, 2445, 2579, 2776, 2932, 3142, 3298, 3539, 3702, 3941, 4139

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..51.

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

J. Bloom and D. Saracino Rook and Wilf equivalence of integer partitions, European J. Combin., 76 (2018), 199-207.

J. Bloom and D. Saracino On Criteria for rook equivalence of Ferrers boards, European J. Combin., 71 (2018), 246-267.

Crossrefs

Cf. A309097, A309098, A309099, A309058.

Sequence in context: A319473 A085894 A354468 * A330640 A319474 A218508

Adjacent sequences: A309191 A309192 A309193 * A309195 A309196 A309197

Keyword

nonn

Author

Jonathan S. Bloom, Jul 16 2019

Extensions

More terms from Alois P. Heinz, Jul 18 2019

Status

approved