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Number Theory Commons

Open Access. Powered by Scholars. Published by Universities.®

2018

Combinatorial identity

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Full-Text Articles in Number Theory

Incomplete Generalized (P; Q; R)-Tribonacci Polynomials, Mark Shattuck, Elif Tan Jun 2018

Incomplete Generalized (P; Q; R)-Tribonacci Polynomials, Mark Shattuck, Elif Tan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider an extension of the tribonacci polynomial, which we will refer to as the generalized (p; q; r)-tribonacci polynomial, denoted by Tn;m(x).We find an explicit formula for Tn;m(x)which we use to introduce the incomplete generalized (p; q; r)-tribonacci polynomials and derive several properties. An explicit formula for the generating function of the incomplete generalized polynomials is determined and a combinatorial interpretation is provided yielding further identities.