According to OEIS A008907 the number of legal tic-tac-toe (or noughts and crosses) positions after n plays, up to rotation and reflection:
{1, 3, 12, 38, 108, 174, 204, 153, 57, 15}
But if I use your code as:
moves[k_]:=Length[VertexList[ShowGraph[k,ClassicStartingBoard]]];
Table[moves[k+1]-moves[k],{k,0,8}]
I get
{3,12,63,270,725,1036,977,344,74}
Does this seem correct ?
