Affiliation:
1. Departamento de Matemáticas, Universidad de Oviedo, Oviedo, Spain
2. Centro Universitario de la Defensa de Zaragoza - IUMA, Zaragoza, Spain
3. Departamento de Matemáticas y Computación, Universidad de La Rioja, Logroño, Spain
Abstract
The weighted Delannoy numbers are defined by the recurrence relation fm,n =
? fm?1,n +? fm,n?1 + ? fm?1,n?1 if mn > 0, with fm,n = ?m?n if nm = 0. In
this work, we study a generalization of these numbers considering the same
recurrence relation but with fm,n = AmBn if nm = 0. More particularly, we
focus on the diagonal sequence fn,n. With some ingenuity, we are able to
make use of well-established methods by Pemantle and Wilson, and by Melczer in
order to determine its asymptotic behavior in the case A, B, ?, ?, ? ? 0. In
addition, we also study its P-recursivity with the help of symbolic
computation tools.
Publisher
National Library of Serbia
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