A135908 - OEIS

%I #11 Jan 25 2015 21:12:08

%S 0,0,0,2,3,5,8,11,17,26,35,53,80,107,161,242,323,485,728,971,1457,

%T 2186,2915,4373,6560,8747,13121,19682,26243,39365,59048,78731,118097,

%U 177146,236195,354293,531440,708587,1062881,1594322,2125763,3188645,4782968,6377291,9565937

%N Clique number of commuting graph of symmetric group S_n.

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

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

%F 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

%t 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 *)

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Mar 07 2008