Restricted occupancy of s kinds of cells and generalized Pascal triangles
Spiros D. Dafnis, Frosso S. Makri, Andreas N. Philippou · The Fibonacci Quarterly · 2007
There are several well-known formulas counting the number of distinct allocations of n indistinguishable objects into m distinguishable cells, each of which has capacity k − 1. In the present paper we generalize four of them by relaxing the assumption that each of the m cells has capacity k – 1 and assuming instead that there are s kinds of cells and each cell of kind i has capacity ki – 1 (i = 1, …, s). A generalization of the Pascal triangles of order k is also discussed.