AN EXTENSION OF SOME RESULTS DUE TO JARDEN

Anthony G. Shannona; Charles K. Cook; Rebecca A. Hillman

doi:10.24297/jam.v9i8.2245

AN EXTENSION OF SOME RESULTS DUE TO JARDEN

Authors

Anthony G. Shannona Faculty of Engineering & IT, University of Technology, Sydney, NSW 2007,
Charles K. Cook Emeritus, University of South Carolina Sumter, Sumter, SC 29150, USA
Rebecca A. Hillman Associate Professor of Mathematics, University of South Carolina Sumter, Sumter, SC 29150, USA

DOI:

https://doi.org/10.24297/jam.v9i8.2245

Keywords:

product sums, shift operators, basic sequences, primordial sequences, fundamental sequences, Fibonacci sequences, Lucas sequences, characteristic equations, Cauchy calculus

Abstract

This paper defines some generalized Fibonacci and Lucas sequences which satisfy arbitrary order linear recurrence relations and which answer a problem posed by Jarden in 1966 about generalizing an elegant result for a connection between even and odd subscripted Fibonacci and Lucas numbers.

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Published

2015-01-07

How to Cite

Shannona, A. G., Cook, C. K., & Hillman, R. A. (2015). AN EXTENSION OF SOME RESULTS DUE TO JARDEN. JOURNAL OF ADVANCES IN MATHEMATICS, 9(8), 2937–2945. https://doi.org/10.24297/jam.v9i8.2245