A085642 Number of columns in the character table of the symmetric group S_n that have zero sum.

0, 1, 1, 2, 3, 6, 8, 12, 17, 26, 35, 49, 66, 92, 121, 161, 211, 280, 360, 466, 596, 766, 968, 1225, 1538, 1935, 2408, 2996, 3707, 4588, 5636, 6918, 8456, 10329, 12552, 15236, 18431, 22275, 26817, 32242, 38661, 46306, 55294, 65942, 78464, 93252, 110561

Offset

1,4

Comments

Conjecture: Equals the number of partitions of n with at least one part congruent to 2 mod 4. - Vladeta Jovovic, Jul 12 2003. This conjecture was established by Christine Bessenrodt and Jorn B. Olsson (olsson(AT)math.ku.dk), Sep 13 2004.

Also number of partitions of n with some odd part repeated. - Vladeta Jovovic, Feb 05 2005

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Christine Bessenrodt and Jorn Olsson, On the sequence A085642

Dominique Gouyou-Beauchamps and Philippe Nadeau, Signed Enumeration of Ribbon Tableaux with Local Rules and Generalizations of the Schensted Correspondence, in Formal Power Series and Algebraic Combinatorics, Nankai University, Tianjin, China, 2007.

Dominique Gouyou-Beauchamps and Philippe Nadeau, Signed enumeration of ribbon tableaux: an approach through growth diagrams, Journal of Algebraic Combinatorics, 2011; DOI 10.1007/s10801-011-0324-2.

Formula

a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*n*sqrt(3)). - Vaclav Kotesovec, Jul 11 2018

Mathematica

Rest[PartitionsP[Range[0, 47]] - CoefficientList[Series[Product[(1+x^(2 k - 1))/(1 - x^(2 k)), {k, 48}], {x, 0, 47}], x]] (* Wouter Meeussen, Dec 20 2017 *)

Crossrefs

Cf. A006950.

Sequence in context: A343820 A133582 A325342 * A270738 A049194 A058298

Adjacent sequences: A085639 A085640 A085641 * A085643 A085644 A085645

Keyword

nonn

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 11 2003

Extensions

Corrected and extended by Vladeta Jovovic, Jul 12 2003

More terms from David Wasserman, Feb 08 2005

Status

approved