  Let the sequence S_m of nonnegative integers be generated by the following
conditions: Set the first term a_0 = 0, and for all k \geq 0, let a_k+1 be the
least integer greater than a_k such that no element of {a_0,...,a_k+1} is the
average of m - 1 distinct other elements. Szekeres gave a closed-form
description of S_3 in 1936, and Layman provided a similar description for S_4
in 1999. We first find closed forms for some similar greedy sequences that
avoid averages in terms not all the same. Then, we extend the closed-form
description of S_m from the known cases when m = 3 and m = 4 to any integer m
\geq 3. With the help of a computer, we also generalize this to sequences that
avoid solutions to specific weighted averages in distinct terms. Finally, from
the closed forms of these sequences, we find bounds for their growth rates.
