Journal of Integer Sequences, Vol. 15 (2012), Article 12.1.4

Some New Properties of Balancing Numbers and Square Triangular Numbers

Refik Keskin and Olcay Karaatlı
Department of Mathematics
Faculty of Arts and Science
Sakarya University
54187 Serdivan


A number N is a square if it can be written as N = n2 for some natural number n; it is a triangular number if it can be written as N = n(n+1)/2 for some natural number n; and it is a balancing number if 8N2 +1 is a square. In this paper, we study some properties of balancing numbers and square triangular numbers.

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(Concerned with sequences A000032 A000045 A000129 A000217 A001108 A001109 A002203 A002378 A003499 A053141.)

Received June 13 2011; revised version received December 2 2011. Published in Journal of Integer Sequences, December 27 2011. Small revision, October 2 2012.

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