Ambiguity in the m-bonacci numeration system
Petra Kocábová, Zuzana Masáková, Edita Pelantová
Abstract
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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