

A309099


Number of partitions of n avoiding the partition (4,3,1).


3



1, 1, 2, 3, 5, 7, 11, 15, 21, 28, 37, 46, 59, 72, 87, 104, 124, 144, 168, 192, 220, 250, 282, 314, 352, 391, 432, 475, 522, 569, 622, 675, 732, 791, 852, 915, 985, 1055, 1127, 1201, 1281, 1361, 1447, 1533, 1623, 1717, 1813, 1909, 2013, 2118, 2227, 2338, 2453
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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..52.
Jonathan Bloom, Nathan McNew, Counting patternavoiding 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), 246267.
J. Bloom and D. Saracino, On Criteria for rook equivalence of Ferrers boards, European J. Combin., 76 (2018), 199207.


CROSSREFS

Cf. A309097, A309098, A309058.
Sequence in context: A280938 A049756 A319472 * A218507 A026813 A008636
Adjacent sequences: A309096 A309097 A309098 * A309100 A309101 A309102


KEYWORD

nonn


AUTHOR

Jonathan S. Bloom, Jul 12 2019


EXTENSIONS

More terms from Alois P. Heinz, Jul 12 2019


STATUS

approved



