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.

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

Author

Mohammad K. Azarian

Keywords

• nonn
• tabf
• less

Examples

			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; ...
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Programs

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 *)