For positive integers i and j, define d_{(i, j)} as follows: d_{(1, j)}=1, d_{(i, 1)}=1 for all i and j, and for i, j>1, d_{(i, j)}=d_{(i-1, j)}+d_{(i, j-1)}+d_{(i-1, j-1)}. Compute the remainder when d_{(3,2016)} is divided by 1000.
For positive integers i and j, define d_{(i, j)} as follows: d_{(1, j)}=1, d_{(i, 1)}=1 for all i and j, and for i, j>1, d_{(i, j)}=d_{(i-1, j)}+d_{(i, j-1)}+d_{(i-1, j-1)}. Compute the remainder when d_{(3,2016)} is divided by 1000.