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

Author

Jonathan S. Bloom, Jul 12 2019

Keywords

• nonn
• changed

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

• Jonathan Bloom and 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.

Programs

PARI

lista(n)=Vec((1+sum(i=3,n,x^i/(1-x^i)+O(x*x^n)))/(1-x-x^2+x^3)) \\ Christian Sievers, Sep 01 2025

Formula

G.f.: (1 + Sum_{i>=3} x^i/(1-x^i)) / (1-x-x^2+x^3). - Christian Sievers, Sep 01 2025

Extensions

More terms from Alois P. Heinz, Jul 12 2019