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
Full paper (PDF, 53 Kb)

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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