A135908 Clique number of commuting graph of symmetric group S_n.

0, 0, 0, 2, 3, 5, 8, 11, 17, 26, 35, 53, 80, 107, 161, 242, 323, 485, 728, 971, 1457, 2186, 2915, 4373, 6560, 8747, 13121, 19682, 26243, 39365, 59048, 78731, 118097, 177146, 236195, 354293, 531440, 708587, 1062881, 1594322, 2125763, 3188645, 4782968, 6377291, 9565937

Offset

0,4

Comments

The graph is empty for n = 0, 1 and 2, so a(n) = 0 by convention (or should it be 1?).

References

A. Iranmanesh and A. Jafarzadeh, On the commuting graph associated with the symmetric and alternating groups, J. Algebra and Applic., 7 (2008), 129-146.

Links

Table of n, a(n) for n=0..44.

Formula

Conjecture: a(n) = a(n-1) + 3*a(n-3) - 3*a(n-4) for n>7; g.f.: -x^3*(3*x^3 - 2*x^2 - x - 2) / ((x-1)*(3*x^3-1)). - Colin Barker, Jul 26 2013

Mathematica

f[n_]:=n+Divisors[n+1][[Length[Divisors[n+1]]-1]]; a=1; Table[a=f[a], {n, 5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 03 2010 *)

Crossrefs

Sequence in context: A370729 A000511 A263710 * A056891 A065462 A062762

Adjacent sequences: A135905 A135906 A135907 * A135909 A135910 A135911

Keyword

nonn

Author

N. J. A. Sloane, Mar 07 2008

Status

approved