## 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

Pell numbers