The q-Calkin–Wilf tree

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Abstract

We define a q-analogue of the Calkin–Wilf tree and the Calkin–Wilf sequence. We show that the nth term f(n;q) of the q-analogue of the Calkin–Wilf sequence is the generating function for the number of hyperbinary expansions of n according to the number of powers that are used exactly twice. We also present formulae for branches within the q-analogue of the Calkin–Wilf tree and predecessors and successors of terms in the q-analogue of the Calkin–Wilf sequence.

Keywords

Calkin–Wilf tree
Calkin–Wilf sequence
Hyperbinary expansion
q-Analogue

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