Discrete Mathematics & Theoretical Computer Science, Vol 9, No 2 (2007)

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Ambiguity in the m-bonacci numeration system

Petra Kocábová, Zuzana Masáková, Edita Pelantová


We study the properties of the function R(m)(n) defined as the number of representations of an integer n as a sum of distinct m-Bonacci numbers F(m)k, given by Fi(m)=2i-1, for i∈ { 1, 2, …, m}, Fk+m(m)=Fk+m-1(m)+Fk+m-2(m) + ⋯ + Fk(m), for k ≥ 1. We give a matrix formula for calculating R(m)(n) from the greedy expansion of n. We determine the maximum of R(m)(n) for n with greedy expansion of fixed length k, i.e. for F(m)k ≤ n

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