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

P Shanmudanantham; C Deepa

doi:10.17485/IJST/v16i45.2103

Article

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

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i45.2103

Year: 2023, Volume: 16, Issue: 45, Pages: 4275-4279

Original Article

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

P Shanmudanantham¹, C Deepa^2*

¹Associate Professor, National College, Affiliated to Bharadhidasan University, Tiruchirappalli, India
²Research Scholar, National College, Tiruchirappalli, India

*Corresponding Author
Email: [email protected]

Received Date:18 August 2023, Accepted Date:14 October 2023, Published Date:06 December 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

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.

Keywords: Carol Numbers, Sum of Squares, Cullan Numbers, Woodall numbers, Kynea numbers

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Copyright

© 2023 Shanmudanantham & Deepa. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)