TY - JOUR
T1 - Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences
AU - Tan, Elif
AU - Leung, Ho Hon
N1 - Publisher Copyright:
© 2020, The Author(s).
PY - 2020/12/1
Y1 - 2020/12/1
N2 - In this paper, we consider a generalization of Horadam sequence { wn} which is defined by the recurrence relation wn= χ(n) wn − 1+ cwn − 2, where χ(n) = a if n is even, χ(n) = b if n is odd with arbitrary initial conditions w, w1 and nonzero real numbers a, b and c. As a special case, by taking the initial conditions 0, 1 and 2, b we define the sequences { un} and { vn} , respectively. The main purpose of this study is to derive some basic properties of the sequences { un} , { vn} and { wn} by using a matrix approach.
AB - In this paper, we consider a generalization of Horadam sequence { wn} which is defined by the recurrence relation wn= χ(n) wn − 1+ cwn − 2, where χ(n) = a if n is even, χ(n) = b if n is odd with arbitrary initial conditions w, w1 and nonzero real numbers a, b and c. As a special case, by taking the initial conditions 0, 1 and 2, b we define the sequences { un} and { vn} , respectively. The main purpose of this study is to derive some basic properties of the sequences { un} , { vn} and { wn} by using a matrix approach.
KW - Bi-periodic Fibonacci sequence
KW - Horadam sequence
KW - Matrix method
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U2 - 10.1186/s13662-020-2507-4
DO - 10.1186/s13662-020-2507-4
M3 - Article
AN - SCOPUS:85077901535
SN - 1687-1839
VL - 2020
JO - Advances in Difference Equations
JF - Advances in Difference Equations
IS - 1
M1 - 26
ER -