On the Inhomogeneous Geometric Line-Sequence

Jack Lee

A chapter in Applications of Fibonacci Numbers, 1999, pp 233-240 from Springer

Abstract: Abstract There have been some recent investigations in the inhomogeneity of the second order recurrence sequence, see for example [1], [2], [3], [6] and [7]. We extend the investigation to include the inhomogeneity also in the corresponding geometric sequence. Consider the line-sequence generated by the recurrence relation $$u_n = cu_{n-2} + bu_{n-1} + k, \ \ n \in z$$ , where c and b are non-zero integers and k the linear inhomogeneous term. We seek the conditions under which the terms of the line-sequence generated by (1.1) also satisfy the inhomogeneous geometric relation $$u_n = xu_{n-1} + g$$ , where x is the geometric ratio and g the geometric inhomogeneous term.

Keywords: 11B39 (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-011-4271-7_23

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DOI: 10.1007/978-94-011-4271-7_23

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