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

Read more

Summary

Introduction

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).

Results
Conclusion

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.