Abstract
In this work, we introduce a further generalization of the Fibonacci-type sequence, namely, generalized Fibonacci-type sequence. We also provide the general solution of nonhomogeneous generalized Fibonacci-type sequence, which can be expressed in terms of the Fibonacci-type numbers.
Highlights
We introduce a further generalization of the Fibonacci-type sequence, namely, generalized Fibonacci-type sequence
We provide the general solution of nonhomogeneous generalized Fibonacci-type sequence, which can be expressed in terms of the Fibonacci-type numbers
The Fibonacci sequence {Fn}∞n=0 is a sequence of numbers, starting with the integer pair 0 and 1, where the value of each element is calculated as the sum of two preceding it
Summary
The Fibonacci sequence {Fn}∞n=0 is a sequence of numbers, starting with the integer pair 0 and 1, where the value of each element is calculated as the sum of two preceding it. We introduce a further generalization of the Fibonacci-type sequence, namely, generalized Fibonacci-type sequence. We provide the general solution of nonhomogeneous generalized Fibonacci-type sequence, which can be expressed in terms of the Fibonacci-type numbers. ∑k i=0 αini with initial conditions was introduced by Asveld (Asveld, 1987).
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