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A006907 Number of zeros in character table of symmetric group S_n.
(Formerly M3394) 		8
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 (list; graph; refs; listen; history; text; internal format)
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: A008995 A111236 A164361 * A305204 A327590 A321344
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

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Last modified August 29 21:13 EDT 2024. Contains 375518 sequences. (Running on oeis4.)