“…The properties of various configurations within the triangle array for the Fibonacci triangle were investigated in [4]. In this section, we examine similar properties for the Narayana triangle.…”
Section: Some Identities Of New Narayana Trianglementioning
confidence: 99%
“…(2) where (3) The Narayana numbers and their properties have been studied by Özkan, Ramirez, Petersen, et al [3][4][5][6][7][8][9][10]. In particular, Petersen [5] places them in the Euler-Macmahon-Carlitz/Riordan combinatorial spectrum.…”
In this paper, inspiring Hosoya’s triangle, we define a new Narayana triangle. Then, we represent this Narayana triangle geometrically on the plane. In addition, we give some identities and properties of the new Narayana triangle.
“…The properties of various configurations within the triangle array for the Fibonacci triangle were investigated in [4]. In this section, we examine similar properties for the Narayana triangle.…”
Section: Some Identities Of New Narayana Trianglementioning
confidence: 99%
“…(2) where (3) The Narayana numbers and their properties have been studied by Özkan, Ramirez, Petersen, et al [3][4][5][6][7][8][9][10]. In particular, Petersen [5] places them in the Euler-Macmahon-Carlitz/Riordan combinatorial spectrum.…”
In this paper, inspiring Hosoya’s triangle, we define a new Narayana triangle. Then, we represent this Narayana triangle geometrically on the plane. In addition, we give some identities and properties of the new Narayana triangle.
In this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled Narayana’s sequence. We give a binomial direct formula for these sequences using graph methods, and also we derive a number of identities. Moreover, we study matrix generators of these sequences and determine connections with the Pascal’s triangle.
“…In recent years, many interesting papers investigating the properties of Narayana numbers and Narayana polynomials have been published, see e.g. [8,12,15,16,18].…”
The hybrid numbers are generalization of complex, hyperbolic and dual numbers. The hybrinomials are polynomials which generalize hybrid numbers. In this paper, we introduce and study the distance Fibonacci hybrinomials, i.e. hybrinomials with coefficients being distance Fibonacci polynomials.
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