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Problem of the Week 832

How Many Sequences?

Fix a positive integer n. How many sequences (a1, a2, ... , an) of positive integers are there with the property that at most i of the terms are greater than n-i, for all i = 0,1,...,n?

Source: Richard Stanley (MIT) posed this problem as a warm-up for a recent talk he gave at Harvey Mudd.

© Copyright 1997 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998