Unformatted text preview: metic function is a discrete analogue of a
linear function dx+a.
6 Strings The data type of a string is nothing but a
sequence of finite length. 7 Recurrence Relations 8 Recurrence Relation
A recurrence relation for a sequence {an}
expresses the term an in terms of previous terms
of the sequence.
The initial conditions for a recursively defined
sequence specify the terms before the
recurrence relation takes effect.
A sequence is called a solution of a recurrence
relation if its terms satisfy the recurrence
relation.
9 Example
Let {an} be the sequence defined by the initial
condition
a0=2
and the recurrence relation
an = an1 + 3
Then a1 =2+3=5, a2=5+3=8, a3=8+3=11,... 10 Fibonacci Sequence
Recall that the Fibonacci sequence is defined by
the initial conditions: f0=0 and f1=1
and the recurrence relation
fn = fn1+fn2
for n >= 2.
Hence, {fn} = {0,1,1,2,3,5,8,13,...}
11 Solving Recurrence Relations
We say that we have solved a recurrence relation
if we can find an explicit formula, called a closed
formula, for the terms of the sequence.
Example: For th...
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 Fall '11
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