Problem of the Week 1031

Counting Combs

Consider the set A = {1, 2, 3, ..., 1031}. In how many ways can A be partitioned into disjoint sets A = B1 ∪ B2 ∪ ... ∪ B_r such that each B_i is an arithmetic progression having 1 or more elements and common difference 2?

Source: Amer Math Monthly January, 2005.

© Copyright 2005 Stan Wagon. Reproduced with permission.