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 = 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.
Full version: pdf,
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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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