A generalization of an Ulam Sequence in which each term is the Sum of two earlier terms in exactly ways. -additive sequences are a further generalization in which each term has exactly representations as the Sum of distinct earlier numbers. It is conjectured that 0-additive sequences ultimately have periodic differences of consecutive terms (Guy 1994, p. 233).

**References**

Finch, S. R. ``Conjectures about -Additive Sequences.'' *Fib. Quart.* **29**, 209-214, 1991.

Finch, S. R. ``Are 0-Additive Sequences Always Regular?'' *Amer. Math. Monthly* **99**, 671-673, 1992.

Finch, S. R. ``On the Regularity of Certain 1-Additive Sequences.'' *J. Combin. Th. Ser. A.* **60**,
123-130, 1992.

Finch, S. R. ``Patterns in 1-Additive Sequences.'' *Experiment. Math.* **1**, 57-63, 1992.

Guy, R. K. *Unsolved Problems in Number Theory, 2nd ed.* New York: Springer-Verlag, pp. 110 and 233, 1994.

Ulam, S. M. *Problems in Modern Mathematics.* New York: Interscience, p. ix, 1964.

© 1996-9

1999-05-26