  As a generalization of the sum of digits function and other digital
sequences, sequences defined as the sum of the output of a transducer are
asymptotically analyzed. The input of the transducer is a random integer in
$[0, N)$. Analogues in higher dimensions are also considered. Sequences defined
by a certain class of recursions can be written in this framework.
  Depending on properties of the transducer, the main term, the periodic
fluctuation and an error term of the expected value and the variance of this
sequence are established. The periodic fluctuation of the expected value is
H\"older continuous and, in many cases, nowhere differentiable. A general
formula for the Fourier coefficients of this periodic function is derived.
Furthermore, it turns out that the sequence is asymptotically normally
distributed for many transducers. As an example, the abelian complexity
function of the paperfolding sequence is analyzed. This sequence has recently
been studied by Madill and Rampersad.
