On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications
In this work, we obtain a new formula for Fibonacci’s family <i>m</i>-step sequences. We use our formula to find the <i>n</i>th term with less time complexity than the matrix multiplication method. Then, we extend our results for all linear homogeneous recurrence &l...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-09-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/7/9/805 |
| Summary: | In this work, we obtain a new formula for Fibonacci’s family <i>m</i>-step sequences. We use our formula to find the <i>n</i>th term with less time complexity than the matrix multiplication method. Then, we extend our results for all linear homogeneous recurrence <i>m</i>-step relations with constant coefficients by using the last few terms of its corresponding Fibonacci’s family <i>m</i>-step sequence. As a computational number theory application, we develop a method to estimate the square roots. |
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| ISSN: | 2227-7390 |