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October 2020 Plane section recurrences in the Pascal pyramid
Hacène Belbachir, Abdelghani Mehdaoui
Rocky Mountain J. Math. 50(5): 1561-1566 (October 2020). DOI: 10.1216/rmj.2020.50.1561

Abstract

This work deals with the plane sections lying over the Pascal pyramid. Any plane section can be defined using two main diagonals with parameters (q1,r1) and (q2,r2). We study the main case r1=r2=1, which corresponds to plane sections crossing all parallel planes to the x axis and intersecting with the integer coordinates of the pyramid. We establish the recurrence relation satisfied by the sequence of numbers counting the sum of elements lying over each plane section.

Citation

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Hacène Belbachir. Abdelghani Mehdaoui. "Plane section recurrences in the Pascal pyramid." Rocky Mountain J. Math. 50 (5) 1561 - 1566, October 2020. https://doi.org/10.1216/rmj.2020.50.1561

Information

Received: 9 October 2018; Revised: 12 October 2019; Accepted: 6 November 2019; Published: October 2020
First available in Project Euclid: 5 November 2020

zbMATH: 07274819
MathSciNet: MR4170671
Digital Object Identifier: 10.1216/rmj.2020.50.1561

Subjects:
Primary: 05A10, 05A19, 11B37, 11B65

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 5 • October 2020
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