Abstract
A recurrence relation for a sequence {a i }, which usually begins with a 0 or a 1, is a formula that defines a n in terms of a 0, a 1, a 2, a 3,..., a n−1, and n for all n greater than some particular integer k, with the terms a 0, a 1,..., a k called initial conditions or boundary conditions. Together with the initial conditions, the recurrence relation provides a recursive definition for the elements of the sequence. This allows us to compute the unique value of a n for each integer n such that n > k. Many examples follow. We are already familiar with several recurrence relations.
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© 2001 Springer Science+Business Media New York
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Martin, G.E. (2001). Recurrence Relations. In: Counting: The Art of Enumerative Combinatorics. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4878-9_6
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DOI: https://doi.org/10.1007/978-1-4757-4878-9_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2915-0
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