%I #18 Aug 15 2019 16:49:26

%S 0,0,0,0,1,2,15,85,650,5800,65243,931258,17182237,414512599,

%T 13161989059

%N Number of connected triangle-free graphs on n nodes with chromatic number 3.

%H Keith M. Briggs, <a href="http://keithbriggs.info/cgt.html">Combinatorial Graph Theory</a>

%e Table of number of connected triangle-free graphs on n nodes with chromatic number k begins:

%e (The first row is the same as the number of connected bipartite graphs on n nodes, A005142)

%e n=...1...2...3...4...5....6....7.....8.....9.....10......11.......12.........13

%e k.-----------------------------------------------------------------------------

%e 2|...0...1...1...3...5...17...44...182...730...4032...25598...212780....2241730 (A005142)

%e 3|...0...0...0...0...1....2...15....85...650...5800...65243...931258...17182237 (the present sequence)

%e 4|...0...0...0...0...0....0....0.....0.....0......0.......1.......23.......1085 (A126741)

%K nonn

%O 1,6

%A _N. J. A. Sloane_, based on email from _Keith Briggs_, Mar 21 2006

%E a(14) from _Michael Sollami_, Jan 29 2012

%E a(15) from _Michael Sollami_, Feb 04 2012