Generalized Fibonacci and Lucas sequences with Pascal-type arrays

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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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
{F0,n} ≡ {Fn} and {F1,n} ≡ {Ln}
and consider
Fm,n = Fm−1, n−1 + Fm−1, n+1, m, n ≥ 1,
as a generalization of the well-known identity
Ln = Fn−1 + Fn+1,
where
Fm,n = Fm,n−1 + Fm, n−2, m ≥ 1, n > 2.

AMS Classification

  • 05A10
  • 11B39

References

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Cite this paper

APA

Cook, 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.

Chicago

Cook, 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.

MLA

Cook, 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.

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