Abstract
An m-pseudo progression is an increasing list of numbers for which there are at most m distinct differences between consecutive terms. This object generalizes the notion of an arithmetic progression. We give two counts for the number of k-term m-pseudo progressions in {1, 2, …, n}. We also provide computer-generated tables of values which agree with both counts and graphs that display the growth rates of these functions. Finally, we present a generating function which counts k-term progressions in {1, 2, …, n} whose differences are all distinct, and we discuss further directions in Ramsey theory.