International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 8, Pages 529-532

Recursive determination of the enumerator for sums of three squares

John A. Ewell

Department of Mathematical Sciences, Northern Illinois University, Dekalb 60115, IL, USA

Received 28 July 1999; Revised 12 September 1999

Copyright © 2000 John A. Ewell. 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.


For each nonnegative integer n, r3(n) denotes the number of representations of n by sums of three squares. Here presented is a two-step recursive scheme for computing r3(n), n0.