On the representation of m as ∑k=−nnϵkk

Abstract

Let A(n,m) be the number of solutions of ∑k=−nnϵkk=m where each ϵk∈{0,1}. We determine the asymptotic behavior of A(n,m) for m=o(n3/2), extending results of van Lint and of Entringer.

Keywords

• Representation
• asymptotic behavior.