Recurrence sequences associated to rays in bi-periodic Pascal's triangle

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Nassima Belaggoun Hacène Belbachir

Abstract

In the present paper, we define a new generalization of Pascal's triangle called the bi-periodic Pascal's triangle. We give the recurrence relation associated with the sum of diagonal elements lying along finite rays in the generalized Pascal triangle.Moreover, we derive their generating function and study the bi-periodic Morgan-Voyce phenomenon. Then, we establish somecombinatorial identities and provide a new explicit formula for the classical Morgan-Voyce sequence. Finally, we find the formula for the partial sums of such sequences.

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How to Cite
Belaggoun, N., & Belbachir, H. (2024). Recurrence sequences associated to rays in bi-periodic Pascal's triangle. Acta Mathematica Universitatis Comenianae, 93(3), 137-156. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/2089/1053
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