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).
s-Additive Sequence
See also
Greedy Algorithm, Stöhr Sequence, Sum-Free Set, Ulam SequenceExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
s-Additive SequenceCite this as:
Weisstein, Eric W. "s-Additive Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/s-AdditiveSequence.html