Geodesic
A matrix dynamics approach to Golomb's recursion
The electronic journal of combinatorics, Tome 4 (1997) no. 1
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In an unpublished note Golomb proposed a family of "strange" recursions of metafibonacci type, parametrized by $k$. Previously we showed that contrary to Golomb's conjecture, for each $k$ there are many increasing solutions, and an explicit construction for multiple solutions was displayed. By reformulating our solution approach using matrix dynamics, we extend these results to a characterization of the asymptotic behaviour of all solutions of the Golomb recursion. This matrix dynamics perspective is also used to construct what we believe is the first example of a "nontrivial" nonincreasing solution, that is, one that is not eventually increasing.
DOI : 10.37236/1301
Classification : 11B37, 11B39
Mots-clés : Golomb recursion, matrix dynamics, metafibonacci recursion, linear recursions 
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     title = {A matrix dynamics approach to {Golomb's} recursion},
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Edward J. Barbeau; John Chew; Stephen Tanny. A matrix dynamics approach to Golomb's recursion. The electronic journal of combinatorics, Tome 4 (1997) no. 1. doi: 10.37236/1301

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