A006907 Number of zeros in character table of symmetric group S_n. (Formerly M3394)

0, 0, 1, 4, 10, 29, 55, 153, 307, 588, 1018, 2230, 3543, 6878, 11216, 20615, 33355, 57980, 90194, 155176, 239327, 395473, 604113, 970294, 1453749, 2323476, 3425849, 5349414, 7905133, 11963861, 17521274, 26472001, 38054619, 56756488, 81683457, 119005220, 170498286, 247619748

Offset

1,4

References

J. McKay, personal communication to N. J. A. Sloane, circa 1991.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..38.

Alexander R. Miller, On parity and characters of symmetric groups, preprint.

Alexander R. Miller, On parity and characters of symmetric groups, J. Combin. Theory Ser. A 162 (2019), 231-240.

Formula

a(n) + A051748(n) + A051749(n) = A001255(n). - R. J. Mathar, Mar 09 2022

Mathematica

a[n_] := Count[FiniteGroupData[{"SymmetricGroup", n}, "CharacterTable"], 0, 2]; Array[a, 10] (* Jean-François Alcover, Oct 08 2016 *)

Prog

(GAP) A006907 := n -> Sum(Irr(CharacterTable("Symmetric", n)), chi -> Number(chi, x->x=0)); # Eric M. Schmidt, Jul 13 2012, simplified Jul 26 2012

Crossrefs

Cf. A006908, A051748, A051749.

Sequence in context: A111236 A164361 A376850 * A305204 A327590 A377824

Adjacent sequences: A006904 A006905 A006906 * A006908 A006909 A006910

Keyword

nonn,nice

Author

Simon Plouffe and N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, May 20 2003

More terms from Eric M. Schmidt, Jul 13 2012

a(36)-a(38) found by Alexander R. Miller (see 2019 reference). - N. J. A. Sloane, Jul 07 2020

Status

approved