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Intrinsic Properties of a Non-Symmetric Number Triangle
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Isabel Cação and Helmuth R. Malonek

CIDMA and Department of Mathematics

University of Aveiro

3810-193 Aveiro

Portugal

M. Irene Falcão

CMAT and Department of Mathematics

University of Minho

4710-057 Braga

Portugal

Graça Tomaz

CIDMA and Department of Mathematics

Polytechnic of Guarda

6300-659 Guarda

Portugal

**Abstract:**

Several authors are currently working on generalized Appell polynomials
and their applications in the framework of hypercomplex function theory
in **R**^{n+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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