Summing a Family of Generalized Pell Numbers

A new family of generalized Pell numbers was recently introduced and studied by Bród ([2]). These numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of generalized Pell numbers can be summed explicitly. For this, as a first step, a power P^𝓁_n is expressed as a linear combination of P_mn. The summation of such expressions is then manageable using generating functions. Since the new family contains a parameter R = 2^r, the relevant manipulations are quite involved, and computer algebra produced huge expressions that where not trivial to handle at times.