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

摘要

We study the properties of the function R(m)(n) defined asthe number of representations of an integer n as a sum ofdistinct m-Bonacci numbers F(m)k, given byFi(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 calculatingR(m)(n) from the greedy expansion of n. We determine themaximum of R(m)(n) for n with greedy expansion of fixedlength k, i.e. for F(m)k ≤ n