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A046534
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First numerator and then denominator of the 1/3-Pascal triangle (by row). To get a 1/3-Pascal triangle, replace "2" in the third row of the Pascal triangle by "1/3" and calculate all other rows as in the Pascal triangle.
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29
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1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 4, 3, 4, 3, 1, 1, 1, 1, 7, 3, 8, 3, 7, 3, 1, 1, 1, 1, 10, 3, 5, 1, 5, 1, 10, 3, 1, 1, 1, 1, 13, 3, 25, 3, 10, 1, 25, 3, 13, 3, 1, 1, 1, 1, 16, 3, 38, 3, 55, 3, 55, 3, 38, 3, 16, 3, 1, 1, 1, 1, 19, 3, 18, 1, 31, 1, 110, 3, 31, 1, 18, 1, 19, 3, 1, 1, 1, 1, 22
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OFFSET
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1,10
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LINKS
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Peter J. C. Moses, Table of n, a(n) for n = 1..10000
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EXAMPLE
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1/1; 1/1 1/1; 1/1 1/3 1/1; 1/1 4/3 4/3 1/1; 1/1 7/3 8/3 7/3 1/1; 1/1 10/3 5/1 5/1 10/3 1/1; 1/1 13/3 25/3 10/1 25/3 13/3 1/1; 1/1 16/3 38/3 55/3 55/3 38/3 16/3 1/1; ...
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MATHEMATICA
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thirdPascal[1]={1}; thirdPascal[2]={1, 1}; thirdPascal[3]={1, 1/3, 1}; thirdPascal[n_] := thirdPascal[n] = Join[{1}, Map[Total, Partition[thirdPascal[n-1], 2, 1]], {1}]; Flatten[Map[Transpose, Transpose[{Numerator[#], Denominator[#]}]&[Map[thirdPascal, Range[20]]]]] (* Peter J. C. Moses, Apr 03 2013 *)
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CROSSREFS
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Sequence in context: A195768 A016465 A122947 * A224489 A131324 A079724
Adjacent sequences: A046531 A046532 A046533 * A046535 A046536 A046537
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KEYWORD
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tabf,nonn,easy
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AUTHOR
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Mohammad K. Azarian
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STATUS
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approved
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