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A046213
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First numerator and then denominator of 1/2-Pascal triangle (by row). To get a 1/2-Pascal triangle, replace "2" in third row of Pascal triangle with "1/2" and calculate all other rows as in Pascal triangle.
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22
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1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 3, 2, 1, 1, 1, 1, 5, 2, 3, 1, 5, 2, 1, 1, 1, 1, 7, 2, 11, 2, 11, 2, 7, 2, 1, 1, 1, 1, 9, 2, 9, 1, 11, 1, 9, 1, 9, 2, 1, 1, 1, 1, 11, 2, 27, 2, 20, 1, 20, 1, 27, 2, 11, 2, 1, 1, 1, 1, 13, 2, 19, 1, 67, 2, 40, 1, 67, 2, 19, 1, 13, 2, 1, 1, 1, 1, 15, 2
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OFFSET
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1,10
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LINKS
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EXAMPLE
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1/1;
1/1 1/1;
1/1 1/2 1/1;
1/1 3/2 3/2 1/1;
1/1 5/2 3/1 5/2 1/1;
1/1 7/2 11/2 11/2 7/2 1/1;
1/1 9/2 9/1 11/1 9/1 9/2 1/1;
1/1 11/2 27/2 20/1 20/1 27/2 11/2 1/1; ...
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MATHEMATICA
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fractionalPascal[1, _] = {1}; fractionalPascal[2, _] = {1, 1}; fractionalPascal[3, frac_] = {1, frac, 1}; fractionalPascal[n_, frac_] := fractionalPascal[n, frac] = Join[{1}, Map[Total, Partition[fractionalPascal[n-1, frac], 2, 1]], {1}]; Flatten[Map[Transpose, Transpose[{Numerator[#], Denominator[#]}]&[Map[fractionalPascal[#, 1/2]&, Range[15]]]]] (* Peter J. C. Moses, Apr 04 2013 *)
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CROSSREFS
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KEYWORD
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nonn,tabf,less
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AUTHOR
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STATUS
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approved
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