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Search: id:A157933
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| A157933 |
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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 |
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+0
1
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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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.
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FORMULA
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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].
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EXAMPLE
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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).
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CROSSREFS
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Adjacent sequences: A157930 A157931 A157932 this_sequence A157934 A157935 A157936
Sequence in context: A117525 A075149 A161618 this_sequence A013915 A136445 A052989
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KEYWORD
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nonn,tabl
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), Mar 16 2009
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