NEO BALANCING NUMBERS

Abstract

If a positive integer $n \geq 2$ is a solution of the equation

\begin{equation*}

1+2+3+ \cdots +(n-1)=(n-1)+(n-0)+(n+1) +(n+2) +\cdots+ (n +r)

\end{equation*}

for some integer $r$, $n$ is called a neo balancing number and $r$ is called a neo balancer corresponding to neo balancing number $n$. The purpose of this paper is to establish a generating function of neo balancing numbers, recurrence relations for neo balancing numbers and an application of neo balancing numbers to a Diophantine equation. Moreover, we prove the relations between neo balancing numbers and balancing numbers.

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