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The paper is concerned with estimating the number  ξ  of ones in triangular arrays consisting of elements of the field  GF (2) which are defined by the bottom row of  s  elements. The elements of each higher row are obtained (as in Pascal triangles) by the summation of pairs of elements from the corresponding lower row. It is shown that there exists a monotone unbounded sequence 0 =  k  0  &lt;  k  1  &lt;  k  2  &lt; ... of rational numbers such that, for any  k  &gt; 0, for sufficiently large  s  the admissible values of  ξ  which are smaller than  ks  or larger than  s ( s  + 1)/3 −  sk /3 are concentrated in neighbourhoods of points  k i s  and  s ( s  + 1)/3 −  sk i  /3,  i  ⩾ 0. The resulting estimates of the neighbourhoods are functions of  i  for each  i  ⩾ 0 and do not depend on  s . The distributions of the numbers of triangles with values  ξ  in these neighbourhoods depend only on the residues of  s  with respect to moduli that depend on  i  ⩾ 0.

Distribution of the extreme values of the number of ones in Boolean analogues of the Pascal triangle