%I A157933
%S A157933 1,3,3,7,10,7,15,25,25,15,31,56,66,56,31,63,119,154,154,119,63,127,246,
%T A157933 337,372,337,246,127,255,501,711,837,837,711,501,255,511,1012,1468,1804,
%U A157933 1930,1804,1468,1012,511
%N A157933 Triangle T[i,j] such that sum_{j=0...i} T[i,j]*x[i,j]/2^i = sum_{k=0...i, 
               j=0...k} x[k,j], if x[k-1,j]=(x[k,j]+x[k,j+1])/2
%C A157933 Rows and columns are numbered starting with 0. Consider a pyramid (triangle) 
               where each element is the mean value of the two elements below. Then 
               the sum of all elements is expressed as linear combination of the 
               elements at the base. This sequence gives the coefficients times 
               the necessary power of 2.
%F A157933 The first and last term in the (i+1)-th row is T[i,0] = 2^(i+1)-1.
%F A157933 The second and penultimate term is T[i,1] = T[i,0] + T[i-1,1].
%e A157933 To get the 3rd row of the triangle, consider the pyramid
%e A157933 __f
%e A157933 _d e
%e A157933 a b c
%e A157933 where d=(a+b)/2, e=(b+c)/2, f=(d+e)/2. Then a+b+c+d+e+f=(7a+10b+7c)/2^2, 
               which yields the row (7,10,7).
%Y A157933 Sequence in context: A117525 A075149 A161618 this_sequence A013915 A136445 
               A052989
%Y A157933 Adjacent sequences: A157930 A157931 A157932 this_sequence A157934 A157935 
               A157936
%K A157933 nonn,tabl
%O A157933 0,2
%A A157933 M. F. Hasler (MHasler(AT)univ-ag.fr), Mar 16 2009