The generalized Pell (p,i)-numbers and their Binet formulas, combinatorial representations, sums

Emrah Kılıç

Chaos, Solitons & Fractals, 2009, vol. 40, issue 4, 2047-2063

Abstract: The theory of generalized Pell p-numbers was introduced by Stakhov and then have been studied by several authors. In this paper, we consider the usual Pell numbers and as similar to the Fibonacci p-numbers, we give fair generalization of the Pell numbers, which we call the generalized Pell (p,i)-numbers for 0⩽i⩽p. First we give relationships between the generalized Pell (p,i)-numbers and give the generating matrices for these numbers. Also we derive the generalized Binet formulas, sums, combinatorial representations and generating function of the generalized Pell p-numbers. Also using matrix methods, we derive an explicit formula for the sums of the generalized Fibonacci p-numbers. Finally, we derive relationships between generalized Pell (p,i)-numbers and their sums and permanents of certain matrices.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:40:y:2009:i:4:p:2047-2063

DOI: 10.1016/j.chaos.2007.09.081

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