On Four Special Cases of Generalized Tribonacci Sequence:  Tribonacci-Perrin, modified Tribonacci, modified Tribonacci-Lucas and adjusted Tribonacci-Lucas Sequences

Yüksel Soykan

Yüksel Soykan Department of Mathematics, Art and Science Faculty, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey

Keywords: Tribonacci numbers, Tribonacci-Lucas numbers, Tribonacci-Perrin numbers, modified Tribonacci numbers, modified Tribonacci-Lucas numbers, adjusted Tribonacci-Lucas numbers.

Abstract

In this paper, we investigate four new special cases, namely, Tribonacci-Perrin, modified Tribonacci, modified Tribonacci-Lucas, adjusted Tribonacci-Lucas sequences, of the generalized Tribonacci sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

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