Complementary equations and Wythoff sequences

Kimberling, Clark

Journal of integer sequences, Tome 11 (2008) no. 3

Résumé

The lower Wythoff sequence $a = (a(n))$ and upper Wythoff sequence $b = (b(n))$ are solutions of many complementary equations $f(a,b) = 0$. Typically, $f(a,b)$ involves composites such as $a(a(n))$ and $a(b(n))$, and each such sequence is treated as a binary word (e.g., $aa$ and $ab$). Conversely, each word represents a sequence and, as such, is a linear combination of $a, b$, and 1, in which the coefficients of $a$ and $b$ are consecutive Fibonacci numbers. For example, $baba = 3a+5b-6$.

Détail

Keywords: complementary equation, complementary sequences, Fibonacci numbers, golden ratio, wythoff array, wythoff sequence