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 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 0
 1, 3, 3, 7, 10, 7, 15, 25, 25, 15, 31, 56, 66, 56, 31, 63, 119, 154, 154, 119, 63, 127, 246, 337, 372, 337, 246, 127, 255, 501, 711, 837, 837, 711, 501, 255, 511, 1012, 1468, 1804, 1930, 1804, 1468, 1012, 511 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. LINKS FORMULA The first and last term in the (i+1)-th row is T[i,0] = 2^(i+1)-1. The second and penultimate term is T[i,1] = T[i,0] + T[i-1,1]. EXAMPLE To get the 3rd row of the triangle, consider the pyramid __f _d e a b c 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). CROSSREFS Sequence in context: A075149 A161618 A202873 * A013915 A136445 A326269 Adjacent sequences:  A157930 A157931 A157932 * A157934 A157935 A157936 KEYWORD nonn,tabl AUTHOR M. F. Hasler, Mar 16 2009 STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)