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Some properties of sums involving Pell numbers. (English) Zbl 1137.05009

The Pell numbers \(P_n\) are defined by \(P_{n+1}= 2P_n+ P_{n-1}\) for \(n\geq 1\) and \(P_0= 0\), \(P_1= 1\), and it is shown that for all positive integers \(n\) the sum \(S_{4n+1}\) of the first \(4n+1\) Pell numbers is a perfect square. Then some identities are given involving Pell numbers and binomial coefficients, and finally two divisibility properties of certain sums of Pell numbers are obtained.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
05A19 Combinatorial identities, bijective combinatorics

Keywords:

Pell numbers
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