Hyperbinary representation

A representation

n = \sum_{i \geq 0} a_{i} 2^{i}

with

a_{i} \in {0, 1, 2}

and only finitely many nonzero coefficients. If

h (n)

counts these representations, then

h (0) = 1

,

h (2 m + 1) = h (m)

, and

h (2 m) = h (m) + h (m - 1)

for

m \geq 1

. The integer parity of

n

determines whether the coefficient of

2^{0}

must be 1 or may be 0 or 2.

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