login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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 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, 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 21 13:00 EDT 2020. Contains 337272 sequences. (Running on oeis4.)