A class of weighted Delannoy numbers

Grau, José ; Oller-Marcén, Antonio ; Varona, Juan

Resumen: The weighted Delannoy numbers are defined by the recurrence relation fm,n = α fm−1,n +β fm,n−1 + γ fm−1,n−1 if mn > 0, with fm,n = α mβ n if nm = 0. In this work, we study a generalization of these numbers considering the same recurrence relation but with fm,n = A mB n 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, α, β, γ ≥ 0. In addition, we also study its P-recursivity with the help of symbolic computation tools.

Idioma: Inglés

DOI: 10.2298/FIL2217985G

Año: 2022

Publicado en: FILOMAT 36, 17 (2022), 5985-6007
ISSN: 0354-5180

Factor impacto JCR: 0.8 (2022)

Categ. JCR: MATHEMATICS rank: 170 / 329 = 0.517 (2022) - Q3 - T2
Categ. JCR: MATHEMATICS, APPLIED rank: 210 / 267 = 0.787 (2022) - Q4 - T3

Factor impacto CITESCORE: 1.4 - Mathematics (Q3)

Factor impacto SCIMAGO: 0.368 - Mathematics (miscellaneous) (Q3)

Tipo y forma: Artículo (Versión definitiva)