[Jyaif]

1/ Convert the number to base 3.

2/ Each digit represents an intersection on the goban, assuming the following mapping: 0 = no stone, 1 = black stone, 2 = white stone.

[tromp]

That would work for all positions regardless of legality, which are in 1-1 correspondence to {0,1,2}^(19*19).

The count above is for legal positions only, i.e. those where every connected group of stones is adjacent to an empty point.