  In a recent paper by Kitaev and Remmel, several formulas for the number of
words of length n avoiding some generalized patterns were established. Each
time the obtained function of n had been found in Sloane's Encyclopedia as the
number of some other objects, but the bijections between the two sets did not
follow from the proof. Kitaev and Remmel stated four open problems on finding
respective bijections. Here we solve two of them, concerning sequences A007070
and A048739.
