Given an integral, increasing, linear-recurrent sequence A with initial term 1, the greedy algorithm may be used on the terms of A to repre- sent all positive integers. For large classes of recurrences, the average digit sum is known to equal c A log n+O(1), where c A is a positive constant that depends on A. This asymptotic result is re-proved with an elementary approach for a class of spe- cial recurrences larger than, or distinct from, that of former papers. The focus is on the constants c A for which, among other items, explicit formulas are provided and minimal values are found, or conjectured, for all special recurrences up to a certain order.