Matrix Representation of Bi-Periodic Jacobsthal Sequence
Sukran Uygun *
Department of Mathematics, Faculty of Science and Arts, Gaziantep University, Gaziantep, Turkey.
Evans Owusu
Department of Mathematics, Faculty of Science and Arts, Gaziantep University, Gaziantep, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we bring into light the matrix representation of bi-periodic Jacobsthal sequence, which we shall call the bi-periodic Jacobsthal matrix sequence. We dene it as
with initial conditions J0 = I identity matrix, 
. We obtained the nth general term of this new matrix sequence. By studying the properties of this new matrix sequence, the well-known Cassini or Simpson's formula was obtained. We then proceed to find its generating function as well as the Binet formula. Some new properties and two summation formulas for this new generalized matrix sequence were also given.
Keywords: Jacobsthal sequence, generating function, Binet formula