Binomial Transform of the Generalized Tribonacci Sequence

Main Article Content

Y¨uksel Soykan

Abstract

In this paper, we define the binomial transform of the generalized Tribonacci sequence and as special cases, the binomial transform of the Tribonacci, Tribonacci-Lucas, Tribonacci-Perrin, modified Tribonacci, modified Tribonacci-Lucas and adjusted Tribonacci-Lucas sequences will be introduced. We investigate their properties in details. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these binomial transforms. Moreover, we give some identities and matrices related with these binomial transforms.

Keywords:
Binomial transform, Tribonacci sequence, Tribonacci numbers, Tribonacci-Lucas sequence, Tribonacci-Lucas numbers, binomial transform of Tribonacci sequence, 3-step Fibonacci sequence.

Article Details

How to Cite
Soykan, Y. (2020). Binomial Transform of the Generalized Tribonacci Sequence. Asian Research Journal of Mathematics, 16(10), 26-55. https://doi.org/10.9734/arjom/2020/v16i1030229
Section
Original Research Article

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