Mathematica - Pure Functional
A pure functional approach
f[a_, b_, c_]:=Grid[Array[If[(s = FindInstance [Abs[p =(2((2k+1)a + #1)-1)]
== (2#2-1), k, Integers])!={},
{"\\", , "/"}[[Sign[p] /. s[[1]]]]] &, 2 a {c, b}]]
Note that Mathematica is solving an equation for finding the function of the straight lines in the diamonds. It's a Diophantine equation in k:
Abs[(2((2 * k + 1)a + x)-1)] == (2 * y -1) (only find solutions for Integer k)
For each element, and then, if a solution is found, deciding the "\" or "/" based on the sign of the lhs of the equation. (in the {"\", , "/"}[[Sign[p] /. s[[1]] part )
Usage
f[2, 2, 2]
Or
Grid[f[2, 2, 2], f[1, 6, 2], f[4, 3, 3]]
for generating all test cases at once
