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

1,10

Links

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

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

Adjacent sequences: A046210 A046211 A046212 * A046214 A046215 A046216

Keyword

nonn,tabf,less

Author

Mohammad K. Azarian

Status

approved