A recurrent algorithm for solving a combinatorial problem on arrangements with restrictions

We consider $N$ groups of elements such that the elements in different groups are distinct and each group consists of $Q$ identical elements. How many ways are there to arrange these $QN$ elements so that the permutation obtained contains exactly $L$ pairs of adjacent identical elements, $0\leq L\leq N(Q-1)$? The particular case $L=0$ corresponds to calculating the number of permutations with no two adjacent identical elements.
We suggest a recurrent algorithm for solving the problem and its generalization to the case where the groups may contain different numbers of elements.