A (-1, 0, 1)-matrix is a matrix whose elements consist only of the numbers -1, 0, or 1. The number of distinct (-1, 0, 1)-n×n matrices (counting row and column permutations, the transpose, and multiplication by -1 as equivalent) having 2n different row and column sums for n = 2, 4, 6, ... are 1, 4, 39, 2260, 1338614, ... (OEIS A049475). For example, the 2×2 matrix is given by [-1 | -1 0 | 1].

alternating sign matrix | C-matrix | integer matrix