Pebbling a Chessboard

This note studies a pebbling problem introduced by M. Kontsevich. One starts with an infinite chessboard covering the first quadrant, with single pebble located in the extreme lower left cell. Moves consist of replacing a pebble in cell (i,j) by two pebbles in cells (i+1,j) and (i,j+1),provided neither of those positions is occupied. It is shown how to determine which configurations are reachable, and asymptotics of the number of reachable configurations are determined.