Journal of Integer Sequences, Vol. 26 (2023), Article 23.4.8

Intrinsic Properties of a Non-Symmetric Number Triangle

Isabel Cação and Helmuth R. Malonek
CIDMA and Department of Mathematics
University of Aveiro
3810-193 Aveiro

M. Irene Falcão
CMAT and Department of Mathematics
University of Minho
4710-057 Braga

Graça Tomaz
CIDMA and Department of Mathematics
Polytechnic of Guarda
6300-659 Guarda


Several authors are currently working on generalized Appell polynomials and their applications in the framework of hypercomplex function theory in Rn+1. A few years ago, two of the authors of this paper introduced a prototype of these generalized Appell polynomials, which heavily draws on a one-parameter family of non-symmetric number triangles 𝒯(n), n ≥ 2. In this paper, we prove several new and interesting properties of finite and infinite sums constructed from entries of 𝒯(n), similar to the ordinary Pascal triangle, which is not a part of that family. In particular, we obtain a recurrence relation for a family of finite sums, analogous to the ordinary Fibonacci sequence, and derive its corresponding generating function.

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(Concerned with sequences A001045 A004736 A007318 A011973 A050605 A103252 A104633 A128099 A283208.)

Received December 19 2022; revised version received April 14 2023. Published in Journal of Integer Sequences, May 14 2023.

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