  We consider a directed abelian sandpile on a strip of size $2\times n$,
driven by adding a grain randomly at the left boundary after every $T$
time-steps. We establish the exact equivalence of the problem of mass
fluctuations in the steady state and the number of zeroes in the ternary-base
representation of the position of a random walker on a ring of size $3^n$. We
find that while the fluctuations of mass have a power spectrum that varies as
$1/f$ for frequencies in the range $ 3^{-2n} \ll f \ll 1/T$, the activity
fluctuations in the same frequency range have a power spectrum that is linear
in $f$.
