  We prove the existence of the limiting distribution for the sequence of
denominators generated by continued fraction expansions with even partial
quotients, which were introduced by F. Schweiger and studied also by C.
Kraaikamp and A. Lopes. Our main result is proven following the strategy used
by Ya. Sinai and C. Ulcigrai in their proof of a similar renewal-type theorem
for Euclidean continued fraction expansions and the Gauss map. The main steps
in our proof are the construction of a natural extension of a Gauss-like map
and the proof of mixing of a related special flow.
