no. 3
Combinatorics/Number theory
A q-analogue for bisnomial coefficients and generalized Fibonacci sequences
[Un q-analogue pour les coefficients bisnomiaux et les suites de Fibonacci généralisées]

Présenté par : the Editorial Board

Belbachir, Hacène1 ; Benmezai, Athmane2, 3
1 USTHB, Faculty of Mathematics, RECITS Laboratory, DG-RSDT, BP 32, El Alia 16111, Bab Ezzouar, Algiers, Algeria
2 University of Dely Brahim, Fac. of Eco. & Manag. Sc., RECITS Laboratory, DG-RSDT, Rue Ahmed Ouaked, Dely Brahim, Algiers, Algeria
3 University of Oran, Faculty of Sciences, BP 1524, ELM Naouer, 31000, Oran, Algeria
Comptes Rendus. Mathématique, Tome 352 (2014) no. 3, pp. 167-171.

Nous proposons une nouvelle variante de q-analogue pour les coefficients binomiaux généralisés appelés coefficients bisnomiaux. Elle est basée sur les suites q-Fibonacci proposées par Cigler.

A new q-analogue of bisnomial coefficients is proposed according to the generalized q-Fibonacci sequence suggested by Cigler's approach.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.01.009
Belbachir, Hacène 1 ; Benmezai, Athmane 2, 3

1 USTHB, Faculty of Mathematics, RECITS Laboratory, DG-RSDT, BP 32, El Alia 16111, Bab Ezzouar, Algiers, Algeria
2 University of Dely Brahim, Fac. of Eco. & Manag. Sc., RECITS Laboratory, DG-RSDT, Rue Ahmed Ouaked, Dely Brahim, Algiers, Algeria
3 University of Oran, Faculty of Sciences, BP 1524, ELM Naouer, 31000, Oran, Algeria 
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     title = {A \protect\emph{q}-analogue for bi\protect\textsuperscript{\protect\emph{s}}nomial coefficients and generalized {Fibonacci} sequences},
     journal = {Comptes Rendus. Math\'ematique},
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Belbachir, Hacène; Benmezai, Athmane. A q-analogue for bisnomial coefficients and generalized Fibonacci sequences. Comptes Rendus. Mathématique, Tome 352 (2014) no. 3, pp. 167-171. doi : 10.1016/j.crma.2014.01.009. http://www.numdam.org/articles/10.1016/j.crma.2014.01.009/

[1] Andrews, G.E.; Baxter, J. Lattice gas generalization of the hard hexagon model III q-trinomials coefficients, J. Stat. Phys., Volume 47 (1987), pp. 297-330

[2] Belbachir, H. Determining the mode for convolution power of discrete uniform distribution, Probab. Eng. Inf. Sci., Volume 25 (2011) no. 4, pp. 469-475

[3] Belbachir, H.; Bencherif, F. Linear recurent sequences and powers of a square matrix, Integers, Volume 6 (2006), p. A12

[4] Belbachir, H.; Benmezai, A. Expansion of Fibonacci and Lucas polynomials: An answer to Prodinger's question, J. Integer Seq., Volume 15 (2012) (Article 12.7.6., 5 pp)

[5] Belbachir, H.; Benmezai, A. An alternative approach to Cigler's q-Lucas polynomials, J. Appl. Math. Comput., Volume 226 (2014), pp. 691-698

[6] Belbachir, H.; Bouroubi, S.; Khelladi, A. Connection between ordinary multinomials, Fibonacci numbers, Bell polynomials and discrete uniform distribution, Ann. Math. Inform., Volume 35 (2008), pp. 21-30

[7] Bollinger, R.C. A note on Pascal T-triangles, Multinomial coefficients and Pascal pyramids, Fibonacci Q., Volume 24 (1986), pp. 140-144

[8] Cigler, J. A new class of q-Fibonacci polynomials, Electron. J. Comb., Volume 10 (2003) (Article R19)

[9] Smith, C.; Hogatt, V.E. Generating functions of central values of generalized Pascal triangles, Fibonacci Q., Volume 17 (1979), pp. 58-67

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