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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.
29
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
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
KEYWORD
tabf,nonn,easy
STATUS
approved