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Özkan, Engin; Yilmaz, Nur Şeyma; Włoch, Andrzej

On \(F_3(k,n)\)-numbers of the Fibonacci type. (English) Zbl 1476.11033

Bol. Soc. Mat. Mex., III. Ser. 27, No. 3, Paper No. 77, 18 p. (2021).
Summary: In this paper, we study a generalization of Narayana’s numbers and Padovan’s numbers. This generalization also includes a sequence whose elements are Fibonacci numbers repeated three times. We give combinatorial interpretations and a graph interpretation of these numbers. In addition, we examine matrix generators and determine connections with Pascal’s triangle.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B65 Binomial coefficients; factorials; \(q\)-identities

Keywords:

generalized Fibonacci numbers; Narayana’s numbers; Padovan’s numbers; generating function; Pascal’s triangle
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\textit{E. Özkan} et al., Bol. Soc. Mat. Mex., III. Ser. 27, No. 3, Paper No. 77, 18 p. (2021; Zbl 1476.11033)
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References:

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