
06269361
j
2014b.00694
Schiffman, Jay L.
Exploring the Fibonacci sequence of order three.
Math. Spectr. 46, No. 2, 6671 (2014).
2014
Applied Probability Trust (APT) c/o University of Sheffield, School of Mathematics and Statistics (SoMaS), Sheffield
EN
I30
F60
Fibonacci sequence
Fibonacci sequence of order three
Summary: The Fibonacci sequence of order three is the sequence of numbers $1,3,10,33,109,\dots$ Each term in this sequence from the third term on is equal to three times the previous term plus the term two places before it. This article will explore ideas such as divisibility and periodicity as well as prime elements in this sequence. We conclude by furnishing a closed formula similar to the Binet formula for the Fibonacci sequence in addition to some palatable number tricks.