Charles K. Cook and A. G. Shannon

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 12, 2006, Number 4, Pages 1—9

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## Details

### Authors and affiliations

Charles K. Cook

*Emeritus, University of South Carolina
Sumter, SC 29150 *

A. G. Shannon

*Warrane College, The University of New South Wales, Kensington 1465, &
Raffles KvB, 99 Mount Street, North Sydney, NSW 2065, Australia*

### Abstract

We re-label the Fibonacci and Lucas sequences respectively by

{*F*_{0,n}} ≡ {*F _{n}*} and {

*F*

_{1,n}} ≡ {

*L*}

_{n}and consider

*F*=

_{m,n}*F*

_{m−1, n−1}+

*F*

_{m−1, n+1},

*m*,

*n*≥ 1,

as a generalization of the well-known identity

*L*=

_{n}*F*

_{n−1}+

*F*

_{n+1},

where

*F*=

_{m,n}*F*

_{m,n−1}+

*F*

_{m, n−2},

*m*≥ 1,

*n*> 2.

### AMS Classification

- 05A10
- 11B39

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## Related papers

## Cite this paper

APACook, C. K., Shannon, A. G. (2006). Generalized Fibonacci and Lucas sequences with Pascal-type arrays. Notes on Number Theory and Discrete Mathematics, 12(4), 1-9.

ChicagoCook, Charles K, & A. G. Shannon. “Generalized Fibonacci and Lucas Sequences with Pascal-type Arrays.” Notes on Number Theory and Discrete Mathematics 12, no. 4 (2006): 1-9.

MLACook, Charles K, & A. G. Shannon. “Generalized Fibonacci and Lucas Sequences with Pascal-type Arrays.” Notes on Number Theory and Discrete Mathematics 12.4 (2006): 1-9. Print.