About Warm-ups Problems News

Problem 12

Posted 07/03/2015
Refresh the webpage if formulas are not shown correctly.
----------------------
Previous    Next
----------------------

A signed-binary matrix is a matrix whose elements are either `-1`, `1` or `0`.
A zero-sum matrix is a matrix such that the sum of each column and each row is zero.

For example, `M=[[-1,0,1],[0,0,0],[1,0,-1]]` is a zero-sum signed-binary matrix.

`a(n)` is the number of zero-sum signed-binary matrices of size `n\times n`.

It is easy to see that `a(1)=1` and `a(2)=3`.

Find `a(n)`.




Back to top