  The change-making problem consists of representing a certain amount of money
with the least possible number of coins, from a given, pre-established set of
denominations. The greedy algorithm works by choosing the coins of largest
possible denomination first. This greedy strategy does not always produce the
least number of coins, except when the set of denominations obeys certain
properties. We call a set of denominations with these properties a greedy set.
If the set of denominations is an infinite sequence, we call it totally greedy
if every prefix subset is greedy. In this paper we investigate some totally
greedy sequences arising from second-order linear recurrences with constant
coefficients, as well as their subsequences, and we prove sufficient conditions
under which these sequences are totally greedy.
