SOME ALGEBRAIC RELATIONS ON INTEGER SEQUENCES INVOLVING OBLONG AND BALANCING NUMBERS

TEKCAN A., Ozkoc A., Erasik M. E.

ARS COMBINATORIA, vol.128, pp.11-31, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 128
  • Publication Date: 2016
  • Journal Name: ARS COMBINATORIA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.11-31
  • Bursa Uludag University Affiliated: Yes

Abstract

Let k >= 0 be an integer. Oblong (pronic) numbers are numbers of the form O-k = k(k+1). In this work, we set a new integer sequence B = B-n(k) defined as B-0 = 0, B-1 = 1 and B-n = O-k Bn-1 - Bn-2 for n >= 2 and then derived some algebraic relations on it. Later, we give some new results on balancing numbers via oblong numbers.