Summing a family of generalized Pell numbers
Abstract
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 Pnl is expressed as a linear combination of Pmn. The summation of such expressions is then manageable using generating functions. Since the new family contains a parameter R=2r, the relevant manipulations are quite involved, and computer algebra produced huge expressions that where not trivial to handle at times.
Keywords
Pell numbers; Binet formula; generating functions
References
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Department of Mathematical Sciences, Stellenbosch University, South Africa South Africa
https://orcid.org/0000-0002-0009-8015
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