International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 1, Pages 77-80
doi:10.1155/S0161171200001885
On the representation of m as ∑k=−nnϵkk
Department of Mathematics, Southern Illinois University at Carbondale, Carbondale 62901-4408, IL, USA
Received 3 September 1998
Copyright © 2000 Lane Clark. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.