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A046213
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.
22
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
OFFSET
1,10
LINKS
EXAMPLE
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; ...
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A185155 A249095 A026536 * A215625 A363096 A260222
KEYWORD
nonn,tabf,less
STATUS
approved