Summing a Family of Generalized Pell Numbers
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AbstractA 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 lnis 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.
2021 ◽
Vol 27
(1)
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pp. 134-137
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2004 ◽
Vol 143
(1-3)
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pp. 72-83
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2020 ◽
Vol 1
(3)
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pp. 112-122