Journal of Integer Sequences, Vol. 21 (2018), Article 18.1.2

Further Results on Paths in an n-Dimensional Cubic Lattice


Rigoberto Flórez
Department of Mathematics and Computer Science
The Citadel
Charleston, SC 29409
USA

Leandro Junes
Department of Mathematics, Computer Science and Information Systems
California University of Pennsylvania
California, PA 15419
USA

José L. Ramírez
Departamento de Matemáticas
Universidad Nacional de Colombia
Bogotá
Colombia

Abstract:

We study paths formed by integer n-tuples in an n-dimensional cubic lattice. We establish some connections between these paths, Riordan arrays, coefficients of Chebyshev polynomials of the second kind, and k-colored Motzkin paths.

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(Concerned with sequences A000108 A000984 A001006 A001700 A002212 A002426 A005572 A005573 A016753 A025230 A052177 A052178 A052179 A081671 A098410 A185132 A207823 A261711.)

Received April 16 2017; revised versions received October 11 2017; November 20 2017. Published in Journal of Integer Sequences, December 20 2017.

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