General Terms of All Almost Balancing Numbers of First and Second Type

TL;DR

This paper establishes formulas linking all almost balancing numbers of two types with balancing and Pell numbers, revealing their interrelations and providing a comprehensive understanding of their properties.

Contribution

It derives general terms for all almost balancing numbers of both types in relation to balancing and Pell numbers, and explores their interconnections.

Findings

Established formulas connecting almost balancing and balancing numbers.

Linked almost balancing numbers to Pell numbers.

Provided a comprehensive framework for understanding these number sequences.

Abstract

In this work, we determined the general terms of all almost balancing numbers of first and second type in terms of balancing numbers and conversely we determined the general terms of all balancing numbers in terms of all almost balancing numbers of first and second type. We also set a correspondence between all almost balancing numbers of first and second type and Pell numbers.