  A new generalization of Pascal's triangle, the so-called hyperbolic Pascal
triangles were introduced in [H.B, L.N, L.Sz: Hyperbolic Pascal triangles]. The
mathematical background goes back to the regular mosaics in the hyperbolic
plane. The alternating sum of elements in the rows was given in the special
case $\{4,5\}$ of the hyperbolic Pascal triangles. In this article, we
determine the alternating sum generally in the hyperbolic Pascal triangle
corresponding to $\{4,q\}$ with $q\ge5$.
