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A180649 The difference A046682 - A180652. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A036414 A234954 A321201 * A191238 A049310 A168561
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

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Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)