##
**
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

Sakarya

Turkey

**Abstract:**

A number *N* is a *square* if it can be written as *N* = *n*^{2} 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 8*N*^{2} +1 is a square.
In this paper, we study some
properties of balancing numbers and square triangular numbers.

**
Full version: pdf,
dvi,
ps,
latex
**

(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.

Return to
**Journal of Integer Sequences home page**