Content deleted Content added
→Equivalent definitions: use \varphi consistently |
Fixed a small error in the formula for determining a particular value in the array |
||
Line 20:
:<math>A_{m,n} = A_{m,n-2}+A_{m,n-1}</math> for <math>n > 2</math>.
The [[Zeckendorf's theorem|Zeckendorf representation]] of any positive integer is a representation as a sum of distinct Fibonacci numbers, no two of which are consecutive in the Fibonacci sequence. As {{harvtxt|Kimberling|1995}} describes, the numbers within each row of the array have Zeckendorf representation that differ by a shift operation from each other, and the numbers within each column have Zeckendorf representations that all use the same smallest Fibonacci number. In particular the entry <math>A_{m,n}</math> of the array is the <math>m</math>th smallest number whose Zeckendorf representation begins with the <math>(n+1)</math>th Fibonacci number.
==Properties==
| |||