Closed-form solution of a general three-term recurrence relation
نویسندگان
چکیده
منابع مشابه
A general two-term recurrence and its solution
We find a general explicit formula for all sequences satisfying a two-term recurrence of a certain kind. This generalizes familiar formulas for the Stirling and Lah numbers.
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The recurrence is significant since if we set ai = 0, bi = i for all i we get the Stirling numbers of the second kind, and if we set ai = bi = i for all i we get the Lah numbers. The Lah numbers count the partitions of an n-set into blocks of size k in which the numbers in each block are ordered. The proof in [1] involves generating functions and is rather long. Here we give a short induction p...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2014
ISSN: 1687-1847
DOI: 10.1186/1687-1847-2014-196