On non-Newtonian balancing type numbers

Anetta Szynal-Liana

Abstract


In this paper, we introduce non-Newtonian balancing type numbers. In non-Newtonian calculus, we examine formulas and identities for classical balancing numbers. We give Binet-type formula for non-Newtonian balancing numbers and the general bilinear index-reduction formula which implies Catalan, Cassini and d’Ocagne identities. Moreover, we give the generating function for balancing numbers in terms of non-Newtonian calculus.

Keywords


Non-Newtonian calculus; balancing numbers; Binet’s formula; Catalan identity

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References


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DOI: http://dx.doi.org/10.17951/a.2025.79.1.105-113
Date of publication: 2025-07-31 20:53:38
Date of submission: 2025-07-24 15:00:34


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