Wythoff array: Difference between revisions

Revision as of 09:17, 11 May 2013

Revision as of 11:58, 30 December 2013

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:<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 ZeckondorfZeckendorf representation that differ by a shift operation from each other, and the numbers within each column have ZeckondorfZeckendorf 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 ZeckondorfZeckendorf representation begins with the <math>n</math>th Fibonacci number.

==Properties==