A study on the sum of ‘n+1’ Consecutive Coral Numbers

Abstract

Objectives: To find new formulas for Sums of n+1 Coral Numbers and its matrix form. Methods: Here an attempt made to communicate the formula for Recursive Matrix form and some of its applications. If applications are also provided. Moreover results are obtained by employing mathematical calculations and algebraic simplifications. Results are established by main theorems and their corollary and matrix representations. Findings: A formula for the Sum of n+1 consecutive Coral numbers is obtained by employing a lemma. Matrix form for the sum and Recursive forms are attained here. The matrix form of sums of n+1 consecutive Cullen Numbers is also gained. In the application part some interesting associations between Special Numbers, Cullen Numbers and Carol Numbers are given. Novelty: In the analysis, entirely new formulae are procured. Matrix representation and its recursive forms are new finding in the area of research. Also, different types of correlations between Carol Numbers and other special numbers are provided.