A006908 Number of nonzero elements in the character table of the symmetric group S_n.

1, 4, 8, 21, 39, 92, 170, 331, 593, 1176, 2118, 3699, 6658, 11347, 19760, 32746, 54854, 90245, 149906, 237953, 387937, 608531, 970912, 1510331, 2380015, 3610620, 5634251, 8474110, 12934092, 19440955, 29291690, 43233800, 64825830, 94779612, 139820232

Offset: 1

Author

Simon Plouffe and N. J. A. Sloane

Keywords

• nonn
• nice

Comments

John McKay (email to N. J. A. Sloane, Apr 23 2013) observes that A061256 and A006908 coincide for a surprising number of terms, and asks for an explanation. - N. J. A. Sloane, May 19 2013

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).

Crossrefs

Cf. A006907, A061256.

Programs

GAP

A006908 := n -> Sum(Irr(CharacterTable("Symmetric", n)), chi -> Number(chi, x->x<>0)); # Eric M. Schmidt, Jul 13 2012, revised Sep 05 2012

Mathematica

a[n_] := Count[FiniteGroupData[{"SymmetricGroup", n}, "CharacterTable"], k_ /; k != 0, 2]; Array[a, 10] (* Jean-François Alcover, Oct 21 2016 *)

Extensions

More terms from Eric M. Schmidt, Jul 13 2012