Binomial Transform of the Generalized Tribonacci Sequence
Asian Research Journal of Mathematics · pp. 26–55 · Published 8 Oct 2020
10.9734/arjom/2020/v16i1030229Abstract
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.
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