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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 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

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