  We consider pyramids made of one-dimensional pieces of fixed integer length a
and which may have pairwise overlaps of integer length from 1 to a. We prove
that the number of pyramids of size m, i.e. consisting of m pieces, equals
(am-1,m-1) for each a >= 2. This generalises a well known result for a = 2. A
bijective correspondence between so-called right (or left) pyramids and a-ary
trees is pointed out, and it is shown that asymptotically the average width of
pyramids is proportional to the square root of the size.
