Sum of Squares of ‘n’ Consecutive Carol Numbers

SHANMUGANANDHAM, P.; DEEPA, C.

doi:10.21123/bsj.2023.8399

Cited by 2 publications

(2 citation statements)

References 6 publications

(11 reference statements)

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“…The sum of squares of 'm + 1 ′ consecutive Carol numbers and its Matrix representation has been investigated in 2023 by Shanmuganandham et. al (12) . And recursive form of sum of squares of n consecutive Carol numbers has also been established.…”

Section: Introductionmentioning

confidence: 98%

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

Shanmudanantham,

Deepa

2023

IJST

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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.

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Section: Introductionmentioning

confidence: 98%

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

Shanmudanantham,

Deepa

2023

IJST

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“…They spoke about the generating functions, Simson formulae, Binet formulas, and summation formulas for these sequences. The sum formulae for the squares of generalized Tribonacci numbers' closed forms were researched by Soykan et al The Padovan, Perrin, Tribonacci, and Tribonacci-Lucas summation formulae as well as additional third order recurrence relations were examined as special examples (10,11) .…”

Section: Introductionmentioning

confidence: 99%

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

Shanmudanantham,

Deepika

2023

IJST

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Objectives: The Objective of this article is to find new formulas for Sums of m+1 Woodall Numbers and its matrix form. Here an attempt made to communicate the formula for Recursive Matrix form and some of its applications. Methods: Theorems are proved using the definitions of Woodall numbers. Some 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 m+1 consecutive Woodall numbers is obtained by utilizing a lemma. Matrix form for the sum and Recursive forms are attained here. The matrix form of sums of m+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 Woodall Numbers and other special numbers are provided.

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Sum of Squares of ‘n’ Consecutive Carol Numbers

Cited by 2 publications

References 6 publications

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

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

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

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