A Family of Fibonacci-like Conditional Sequences
نویسندگان
چکیده
Let {ai,j} be real numbers for 0 6 i 6 r 1 and 1 6 j 6 2, and define a sequence {vn} with initial conditions v0, v1 and conditional linear recurrence relation vn = at,1vn 1 + at,2vn 2 where n ⌘ t (mod r) (n > 2). The sequence {vn} can be viewed as a generalization of many well-known integer sequences, such as Fibonacci, Lucas, Pell, Jacobsthal, etc. We find explicitly a linear recurrence equation which is satisfied by {vn}, generating functions, matrix representations and extended Binet’s formulas for {vn} in terms of a generalized continuant.
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تاریخ انتشار 2013