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Behera, Adikanda; Ray, Prasanta Kumar

On the properties of balancing and Lucas-balancing \(p\)-numbers. (English) Zbl 1523.11027

Iran. J. Math. Sci. Inform. 17, No. 2, 147-163 (2022).
Summary: The main goal of this paper is to develop a new generalization of balancing and Lucas-balancing sequences namely balancing and Lucas-balancing \(p\)-numbers and derive several identities related to them. Some combinatorial forms of these numbers are also presented.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B83 Special sequences and polynomials

Keywords:

balancing \(p\)-numbers; Lucas-balancing \(p\)-numbers; incomplete balancing \(p\)-numbers; incomplete Lucas-balancing \(p\)-numbers
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References:

[1] A. Behera, G. K. Panda, On the Square Roots of Triangular Numbers, Fibonacci Quar-terly, 37(2), (1999), 98-105. · Zbl 0962.11014
[2] A. Bérczes, K. Liptai, I. Pink, On Generalized Balancing Sequences, Fibonacci Quarterly, 48(2), (2010), 121-128. · Zbl 1211.11015
[3] P. Catarino, H. Campos, P. Vasco, On Some Identities for Balancing and Cobalancing Numbers, Annales Mathematicae et Informaticae, 45, (2015), 11-24. · Zbl 1349.11022
[4] T. Kovacs, K. Liptai, P. Olajos, On (a, b)-Balancing Numbers, Publicationes Mathemat-icae Debrecen, 77(3-4), (2010), 485-498. · Zbl 1240.11053
[5] K. Liptai, F. Luca, A. Pintér, L. Szalay, Generalized Balancing Numbers, Indagationes Mathematicae, 20(1), (2009), 87-100. · Zbl 1239.11035
[6] G. K. Panda, P. K. Ray, Cobalancing Numbers and Cobalancers, International Journal of Mathematics and Mathematical Sciences, 2005(8), (2005), 1189-1200. · Zbl 1085.11017
[7] B. K. Patel, N. Irmak, P. K. Ray, Incomplete Balancing and Lucas-Balancing Numbers, Mathematical Reports, 20(1), (2018), 59-72. · Zbl 1399.11045
[8] A. Pintér, H. M. Srivastava, Generating Functions of the Incomplete Fibonacci and Lucas Numbers, Rendiconti del Circolo Matematico di Palermo, 48(3), (1999), 591-596. · Zbl 0934.11008
[9] P. K. Ray, Balancing Polynomials and Their Derivatives, Ukrainian Mathematical Jour-nal, 69(4), (2017), 646-663. · Zbl 1485.11037
[10] H. M. Srivastava, H. L. Manocha, A Treatise on Generating Functions, Halsted pres (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984. · Zbl 0535.33001
[11] T. Szakács, Multiplying Balancing Numbers, Acta Universitatis Sapientiae, Mathemat-ica, 3(1) (2011), 90-96. · Zbl 1257.11004
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