May 2024
Intermediate to advanced
332 pages
15h 45m
English
Content preview from Discrete Mathematics
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-----------------------------·COUNTING
241
The
numbers
in
this sequence are called Fibonacci numbers.
We
see that equation (14), together with the special values F
0
= 0 and F
1
= 1, uniquely determine the
Fibonacci numbers.
Thus
we
can
consider (14), together with F
0
= 0
and
F
1
= 1, as the definition
of
these
numbers. This
may
seem
as a somewhat unusual definition: instead
of
telling what
Fn
is (say,
by
a formula),
we
just
give a rule that computes
each
Fibonacci
number
from
the two previous numbers,
and
specify the first
two
values.
Such
a definition is called a recurrence.
It
is
quite similar
in
spirit to induction (except that
it
is
not ...
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