On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications

On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications

In this work, we obtain a new formula for Fibonacci&#8217;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...

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Bibliographic Details
Main Authors: Monther Rashed Alfuraidan, Ibrahim Nabeel Joudah
Format: Article
Language:English
Published: MDPI AG 2019-09-01
Series:Mathematics
Subjects:
Fibonacci’s <i>m</i>-step numbers
time complexity
linear homogeneous recurrence relations
Online Access:https://www.mdpi.com/2227-7390/7/9/805
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spelling doaj-bf99e4e962f2438a88e9083e243765312020-11-25T01:20:33ZengMDPI AGMathematics2227-73902019-09-017980510.3390/math7090805math7090805On a New Formula for Fibonacci’s Family m-step Numbers and Some ApplicationsMonther Rashed Alfuraidan0Ibrahim Nabeel Joudah1Department of Mathematics &amp; Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematics &amp; Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaIn this work, we obtain a new formula for Fibonacci&#8217;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&#8217;s family <i>m</i>-step sequence. As a computational number theory application, we develop a method to estimate the square roots.https://www.mdpi.com/2227-7390/7/9/805Fibonacci’s <i>m</i>-step numberstime complexitylinear homogeneous recurrence relations
collection DOAJ
language English
format Article
sources DOAJ
author Monther Rashed Alfuraidan
Ibrahim Nabeel Joudah
spellingShingle Monther Rashed Alfuraidan
Ibrahim Nabeel Joudah
On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications
Mathematics
Fibonacci’s <i>m</i>-step numbers
time complexity
linear homogeneous recurrence relations
author_facet Monther Rashed Alfuraidan
Ibrahim Nabeel Joudah
author_sort Monther Rashed Alfuraidan
title On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications
title_short On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications
title_full On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications
title_fullStr On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications
title_full_unstemmed On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications
title_sort on a new formula for fibonacci’s family m-step numbers and some applications
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-09-01
description In this work, we obtain a new formula for Fibonacci&#8217;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&#8217;s family <i>m</i>-step sequence. As a computational number theory application, we develop a method to estimate the square roots.
topic Fibonacci’s <i>m</i>-step numbers
time complexity
linear homogeneous recurrence relations
url https://www.mdpi.com/2227-7390/7/9/805
work_keys_str_mv AT montherrashedalfuraidan onanewformulaforfibonaccisfamilymstepnumbersandsomeapplications
AT ibrahimnabeeljoudah onanewformulaforfibonaccisfamilymstepnumbersandsomeapplications
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