p. 129 - 140 Counting all equilateral triangles in {0, 1, ..., n}3 E. J. Ionascu Received: January 3, 2007; Accepted: September 21, 2007 Abstract. We describe a procedure of counting all equilateral triangles in the three dimensional space whose coordinates are allowed only in the set {0, 1, ..., n}3. This sequence is denoted here by ET(n) and it has the entry A102698 in "The On-Line Encyclopedia of Integer Sequences". The procedure is implemented in Maple and its main idea is based on the results in [3]. Using this we calculated the values ET(n) for n = 1 ... 55 extending previous calculations known for n £ 34. Some facts and conjectures about this sequence are stated. The main conjecture raised here is that limn ® ¥((ln ET(n)) / (ln n + 1)) exists. Keywords: diophantine equations; integers. AMS Subject classification: Primary: 11B99; Secondary: 11D09, 11C08. PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2008, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |