A reduced formula for the precise number of (0,1)-matrices in A(R,S)

A formula that calculates the number of n×m matrices in A(R,S) was presented by Wang (Sci. sinica Ser. A 1 (1988) 1). This formula has 2n−2n variables. Later, in 1998, a reduced formula was proposed by Wang and Zhang, in which the number of involved variables was reduced to only 2n−1−n. The reduction in the number of variables is important, but it continues being of order 2n. In this paper a new reduced formula is presented. This formula contains only (n−2)(n−1)/2 variables, that is, of order n2.