The distribution of elements in automatic double sequences Original Research Article

Let image be a q-automatic double sequence over a finite set image. Let image and assume that the number image of gʹs in the nth row of A is finite for each n. We provide a formula for image as a product of matrices according to the digits in the base q expansion of n. This formula generalizes several results on Pascalʹs triangle modulo a prime and on recurrence double sequences. It allows us to relate the asymptotic typical behavior of image to a certain Lyapunov exponent. In some cases we determine this exponent exactly.