Abstract
We have explored a range of enumerative problems by finding a recurrence relation that the corresponding count satisfies. This means that once we have some initial terms, we can progressively calculate more. We have also developed a way to convert some recurrence relations into a generating function. If we can manipulate the generating function and then expand it as a power series that enables us to give explicit expressions for the count by reading off the coefficient of a particular power of the indeterminate used. This last step is the focus of this chapter. Along the way we also explore the different recurrences satisfied by the corresponding sequence.
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© 2011 Springer-Verlag London Limited
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Camina, A., Lewis, B. (2011). Working with Generating Functions. In: An Introduction to Enumeration. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-0-85729-600-9_3
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DOI: https://doi.org/10.1007/978-0-85729-600-9_3
Publisher Name: Springer, London
Print ISBN: 978-0-85729-599-6
Online ISBN: 978-0-85729-600-9
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