## The Zeckendorf array equals the Wythoff array.(English)Zbl 0828.11009

It is known that every natural $$n$$ is uniquely a sum of nonconsecutive Fibonacci numbers, the Zeckendorf representation of $$n$$. This representation can be arranged in the Zeckendorf array $$Z(i,j)$$ where the column $$j$$ is the increasing sequence of all $$n$$ the least term in its Zeckendorf representation being $$F_{j + 1}$$. The Wythoff array $$W(i,j)$$ was introduced by D. R. Morrison [The Fibonacci sequence, Collect. Manuscr., 18th Anniv. Vol., 134-136 (1980; Zbl 0531.05018)]. The author now shows that the Zeckendorf array equals the Wythoff array and gives some other results concerning generalized Zeckendorf arrays.

### MSC:

 11B37 Recurrences 05A10 Factorials, binomial coefficients, combinatorial functions

Zbl 0531.05018