A180649 The difference A046682 - A180652.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 1, 0, 2, 3, 1, 3, 5, 4, 3, 5, 5, 4, 10, 5, 9, 11, 7, 12, 17, 15, 19, 28, 19, 27, 33, 30, 32, 60, 30, 45, 56, 50, 51

Offset

0,18

Comments

A046682 is a bound on the number of different multisets of hook lengths for partitions of n, A180652 is the actual count. So this sequence looks at collisions.

Links

Table of n, a(n) for n=0..52.

Example

It is trivial (by conjugation) that [6, 3, 3, 2] and [4, 4, 3, 1, 1, 1] have the same multiset of hook lengths. Similarly, the pair [5, 5, 2, 1, 1] and [5, 3, 2, 2, 2] are conjugate, so they have the same multiset of hook lengths. What is nontrivial is that those two multisets are the same, explaining the nonzero entry when n=14.

Crossrefs

Cf. A046682, A180652.

Sequence in context: A036414 A234954 A321201 * A191238 A049310 A168561

Adjacent sequences: A180646 A180647 A180648 * A180650 A180651 A180652

Keyword

nonn

Author

Paul-Olivier Dehaye (pdehaye(AT)math.ethz.ch), Sep 14 2010

Extensions

a(41)-a(52) from Alois P. Heinz, Mar 22 2018

Status

approved