Geodesic
Recurrence sequences associated to rays in bi-periodic Pascal's triangle
Nassima Belaggoun1 ; Hacène Belbachir2 ; Nassima Belaggoun ; Hacène Belbachir
1Faculty of Mathematics, RECITS Laboratory, University of Science and Technology Houari Boumediene (USTHB), El Alia, 16111, Bab Ezzouar, Algiers, Algeria; CERIST (Research Center on Scientific and Technical Information), Ben Aknoun, Algiers, Algeria
2Faculty of Mathematics, RECITS Laboratory, University of Science and Technology Houari Boumediene (USTHB), El Alia, 16111, Bab Ezzouar, Algiers, Algeria
Acta mathematica Universitatis Comenianae, Tome 93 (2024) no. 3, pp. 137-156 
Nassima Belaggoun; Hacène Belbachir; Nassima Belaggoun; Hacène Belbachir. Recurrence sequences associated to rays in bi-periodic Pascal's triangle. Acta mathematica Universitatis Comenianae, Tome 93 (2024) no. 3, pp. 137-156. http://geodesic.mathdoc.fr/item/AMUC_2024_93_3_a1/
@article{AMUC_2024_93_3_a1,
     author = {Nassima Belaggoun and Hac\`ene Belbachir and Nassima Belaggoun and Hac\`ene Belbachir},
     title = { Recurrence sequences associated to rays in bi-periodic {Pascal's} triangle},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {137--156},
     year = {2024},
     volume = {93},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2024_93_3_a1/}
}
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Voir la notice de l'article provenant de la source Comenius University

In the present paper, we define a new generalization of Pascal's triangle called the bi-periodic Pascal's triangle. We give the recurrence relation associated with the sum of diagonal elements lying along finite rays in the generalized Pascal triangle.Moreover, we derive their generating function and study the bi-periodic Morgan-Voyce phenomenon. Then, we establish somecombinatorial identities and provide a new explicit formula for the classical Morgan-Voyce sequence. Finally, we find the formula for the partial sums of such sequences.