This study examines a statistic called levels in baryiamonds.Generating functions are found that count the total number of four different kinds of levels in baryiamonds according to the number of cells and the perimeter.As a consequence, by singularity analysis, the average number of each type of levels over all baryiamonds with either n cells or having perimeter n, as n , is studied.
Toufik Mansour (Sun,) studied this question.