  We formulate a mean-field-like theory of long-range correlated $L$-alphabets
sequences, which are actually systems with $(L-1)$ independent parameters.
Depending on the values of these parameters, the variance on the average number
of any given symbol in the sequence shows a linear or a superlinear dependence
on the total length of the sequence. We present exact solution to the
four-alphabets and three-alphabets sequences. We also demonstrate that a
mapping of the given sequence into a smaller alphabets sequence (namely, a {\it
coarse-graining} process) does not necessarily imply that long-range
correlations found in the latter would correspond to those of the former.
