Abstract
Some Identities Involving the Generalized Lucas Numbers
Highlights
In the theory of numbers, the Fibonacci sequence has been always fertile ground for the mathematicians
There are several ways in which it has been generalized. One of these ways is by preserving the initial conditions and changing the recurrence relation
{ } generalizations of the Lucas sequence is the class of sequences
Summary
In the theory of numbers, the Fibonacci sequence has been always fertile ground for the mathematicians. The terms of the sequence of Lucas numbers {Ln } can be obtained by L0 = 2, L1 =1 and the recurrence relation Ln = Ln−1 + Ln−2 ; for n ≥ 2 . One of these ways is by preserving the initial conditions and changing the recurrence relation. Whereas one more way is to preserve the recurrence relation and alternate the initial conditions.
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