Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences
In this paper, we consider a generalization of Horadam sequence { w n } which is defined by the recurrence relation w n = χ ( n ) w n − 1 + c w n − 2 , where χ ( n ) = a if n is even, χ ( n ) = b if n is odd with arbitrary initial conditions w 0 , w 1 and nonzero real numbers a , b and c . As a spec...
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| Published in | Advances in difference equations Vol. 2020; no. 1; pp. 1 - 11 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
14.01.2020
Springer Nature B.V SpringerOpen |
| Subjects | |
| Online Access | Get full text |
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| Summary: | In this paper, we consider a generalization of Horadam sequence
{
w
n
}
which is defined by the recurrence relation
w
n
=
χ
(
n
)
w
n
−
1
+
c
w
n
−
2
, where
χ
(
n
)
=
a
if
n
is even,
χ
(
n
)
=
b
if
n
is odd with arbitrary initial conditions
w
0
,
w
1
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
{
u
n
}
and
{
v
n
}
, respectively. The main purpose of this study is to derive some basic properties of the sequences
{
u
n
}
,
{
v
n
}
and
{
w
n
}
by using a matrix approach. |
|---|---|
| ISSN: | 1687-1847 1687-1839 1687-1847 |
| DOI: | 10.1186/s13662-020-2507-4 |