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A NEW DIRECTION OF FIBONACCI SEQUENCE MODIFICATION
2006
NNTDM
unpublished
The Fibonacci sequence 0,1,1,2,3,5,... is an object of different modifications and extensions. In [1,2] four different ways of constructing two sequences {α i } ∞ i=0 and {β i } ∞ i=0 are described and called 2-Fibonacci sequences (or 2-F-sequences). The four schemes are the following α 0 = a, β 0 = b, α 1 = c, β 1 = d α n+2 = β n+1 + β n , n ≥ 0 β n+2 = α n+1 + α n , n ≥ 0 α 0 = a, β 0 = b, α 1 = c, β 1 = d α n+2 = α n+1 + β n , n ≥ 0 β n+2 = β n+1 + α n , n ≥ 0 α 0 = a, β 0 = b, α 1 = c, β 1
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