Special Matrix

A matrix whose entries satisfy

$$a_{ij}=\cases{ 0 & if $j>i+1$\cr -1 & if $j=i+1$\cr 0 \hbox{ or } 1 & if $j\leq i$.\cr}$$

There are $2^{n-1}$ special Minimal Matrices of size $n\times n$.

References

Knuth, D. E. ``Problem 10470.'' Amer. Math. Monthly 102, 655, 1995.