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Abstract for Ed Barbeau and Steve Tanny, On a Strange Recursion of Golomb

Golomb proposed a family of ``strange''
recursions of metafibonacci type, parameterized by $k$,
and, for each $k$, identified what he speculated was the
unique increasing solution. We show that, to the contrary,
there are many increasing solutions for each $k$, and we
indicate explicitly how to construct them. We also provide some
additional general results concerning the nature of the strictly
increasing solutions for this unusual family of recursions.


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