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# lecture31 - Lecture 31 Linear Recurrence Relations...

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Lecture 31 Linear Recurrence Relations

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Recurrence relations A recurrence relation for the sequence {a(n)} is an equation that expresses a(n) in terms of previous elements in the sequence a(n) = 2*a(n-1) A sequence is called a solution of a recurrence relation if its terms satisfy the relation 1,2,4,8,16, …
Linear Recurrence Relations A linear, homogenous relation of degree k with constant coefficients k n k n n n a c a c a c a ... 2 2 1 1

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Examples Not linear Not homogenous Non-constant coefficients Degree 4 2 1 n n n a a a n a a a n n n 2 1 2 1 2 n n n a na a 4 2 n n a a
Linear Recurrence Relations Basic approach is to look for a solution of the form a n =r n . k n k n n n a c a c a c a ... 2 2 1 1

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Plugging in a n =r n yields Diving everything by r n-k , we get the characteristic equation k n k n n n r c r c r c r ... 2
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lecture31 - Lecture 31 Linear Recurrence Relations...

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