A046534 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 with "1/3" and calculate all other rows as in the Pascal triangle.

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

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 1/3 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; ...

Mathematica

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 *)

Crossrefs

Sequence in context: A372692 A363925 A231147 * A224489 A318933 A361239

Adjacent sequences: A046531 A046532 A046533 * A046535 A046536 A046537

Keyword

tabf,nonn,easy

Author

Mohammad K. Azarian

Status

approved