# counting triangle free graphs

Given $n$, the number of vertices, what is the number of triangle-free simple graphs on $n$ vertices (or asymptotically)?

A more difficult problem is, given $n$, $m$, what is the number of triangle-free simple graphs on $n$ vertices with $\le m$ edges (or asymptotically)?

1, 2, 3, 7, 14, 38, 107, 410, 1897, 12172, 105071, 1262180, 20797002, 467871369, 14232552452