A generalization to almost balancing and cobalancing numbers using triangular numbers

Abstract

A generalization of almost balancing numbers is studied using triangular numbers as the difference between the left and right hand sides of the defining equation of balancing numbers. In case of almost balancing numbers, this difference is kept 1, which is the first triangular number. Some specific representations of these numbers in terms of balancing and balancing related numbers are established and few more results with triangular, square triangular, balancing and balancing related numbers are also studied so as to generalize the identities obtained by A. Tekcan.