<s>
In	O
mathematics	O
,	O
the	O
Fibonacci	B-Algorithm
polynomials	I-Algorithm
are	O
a	O
polynomial	O
sequence	O
which	O
can	O
be	O
considered	O
as	O
a	O
generalization	O
of	O
the	O
Fibonacci	B-Algorithm
numbers	I-Algorithm
.	O
</s>
<s>
The	O
polynomials	O
generated	O
in	O
a	O
similar	O
way	O
from	O
the	O
Lucas	B-Algorithm
numbers	I-Algorithm
are	O
called	O
Lucas	B-Algorithm
polynomials	I-Algorithm
.	O
</s>
<s>
These	O
Fibonacci	B-Algorithm
polynomials	I-Algorithm
are	O
defined	O
by	O
a	O
recurrence	O
relation	O
:	O
</s>
<s>
The	O
Lucas	B-Algorithm
polynomials	I-Algorithm
use	O
the	O
same	O
recurrence	O
with	O
different	O
starting	O
values	O
:	O
</s>
<s>
The	O
Fibonacci	B-Algorithm
polynomials	I-Algorithm
form	O
a	O
sequence	O
of	O
orthogonal	O
polynomials	O
with	O
and	O
.	O
</s>
<s>
The	O
first	O
few	O
Fibonacci	B-Algorithm
polynomials	I-Algorithm
are	O
:	O
</s>
<s>
The	O
first	O
few	O
Lucas	B-Algorithm
polynomials	I-Algorithm
are	O
:	O
</s>
<s>
The	O
Fibonacci	O
and	O
Lucas	B-Algorithm
numbers	I-Algorithm
are	O
recovered	O
by	O
evaluating	O
the	O
polynomials	O
at	O
x	O
=	O
1	O
;	O
Pell	O
numbers	O
are	O
recovered	O
by	O
evaluating	O
Fn	O
at	O
x	O
=	O
2	O
.	O
</s>
<s>
then	O
F(n,k )	O
is	O
the	O
number	O
of	O
ways	O
an	O
n−1	O
by	O
1	O
rectangle	O
can	O
be	O
tiled	O
with	O
2	O
by	O
1	O
dominoes	B-Operating_System
and	O
1	O
by	O
1	O
squares	O
so	O
that	O
exactly	O
k	O
squares	O
are	O
used	O
.	O
</s>
