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On the Inhomogeneous Geometric Line-Sequence

In: Applications of Fibonacci Numbers

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  • Jack Lee

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.

Suggested Citation

  • Jack Lee, 1999. "On the Inhomogeneous Geometric Line-Sequence," Springer Books, in: Fredric T. Howard (ed.), Applications of Fibonacci Numbers, pages 233-240, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-4271-7_23
    DOI: 10.1007/978-94-011-4271-7_23
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