s-Additive Sequence

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.

Finch, S. R. "Stolarsky-Harborth Constant." §2.16 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 145-151, 2003.

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.