Journal of Integer Sequences, Vol. 20 (2017), Article 17.1.8

Fibonacci and Lucas Sedenions


Göksal Bilgici
Department of Computer Education and Instructional Technology
Education Faculty
Kastamonu University
Kastamonu, 37100
Turkey

Ümit Tokeşer and Zafer Ünal
Department of Mathematics
Faculty of Arts and Sciences
Kastamonu University
Kastamonu, 37150
Turkey

Abstract:

The sedenions form a 16-dimensional non-associative and non-commutative algebra over the set of real numbers. In this paper, we introduce the Fibonacci and Lucas sedenions. We present generating functions and Binet formulas for the Fibonacci and Lucas sedenions, and derive adaptations for some well-known identities of Fibonacci and Lucas numbers.

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(Concerned with sequences A000032 A000045.)

Received July 13 2016; revised versions received December 1 2016; December 27 2016. Published in Journal of Integer Sequences, December 27 2016.

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