Elsevier

Discrete Mathematics

Volume 308, Issue 18, 28 September 2008, Pages 4069-4078
Discrete Mathematics

Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas

https://doi.org/10.1016/j.disc.2007.07.106Get rights and content
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Abstract

Motivated by the resemblance of a multivariate series identity and a finite analogue of Euler's pentagonal number theorem, we study multiple extensions of the latter formula. In a different direction we derive a common extension of this multivariate series identity and two formulas of Lucas. Finally we give a combinatorial proof of Lucas’ formulas.

MSC

05A10
05A30

Keywords

q-Binomial coefficient
q-Chu–Vandermonde formula
Euler's pentagonal number theorem
Lucas’ formulas

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