A Study on the Sum of ‘m+1’ Consecutive Cullen Numbers

Objectives: To discover new formulae for the matrix form of the sum of m+1 Cullen numbers. This is an effort to explain the Recursive Matrix form formula and a few of its uses. Methods: Conclusions derived from theorems and the matching matrix representations of them. Additionally, a few apps are offered. The terminology of Cullen Numbers are utilised to demonstrate the main theorems. Additionally, algebraic simplifications and mathematical computations are used to derive the findings. Findings: A lemma is used to construct the formula for the Sum of m+1 consecutive Cullen Numbers. Here, the recursive and sum forms are obtained in matrix form. It also obtains the matrix representation of the sums of m+1 successive Cullen Numbers. Several intriguing correlations among Special Numbers, Cullen Numbers, and Carol Numbers are provided in the application section. Novelty: New formulas are obtained for the analysis. Research has recently discovered matrix representation with its recursive versions. Furthermore, there are many relationships between Cullen Numbers along with other peculiar numbers. Keywords: Cullen Numbers, Carol Numbers, Woodall Numbers, Sum of Cullen Number