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International Journal of Mathematical Education in Science and Technology Volume 43, 2012 - Issue 6
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Classroom Notes

Fibonacci–Pell hybridities

Thomas Koshy Department of Mathematics, Framingham State University, 100 State Street, Framingham, MA 01701-9101, USACorrespondence[email protected]
&
Zhenguang Gao Department of Computer Science, Framingham State University, Framingham, MA 01701-9101, USA
Pages 779-783 | Received 04 May 2011, Published online: 12 Oct 2011
 
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Abstract

We develop a recurrence satisfied by the Fibonacci and Pell families. We then use it to find explicit formulae and generating functions for the hybrids F n P n , L n P n , F n Q n and L n Q n , where F n , L n , P n and Q n denote the nth Fibonacci, Lucas, Pell and Pell–Lucas numbers, respectively. The recurrence enables us to find such relations for and .

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