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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 (list; graph; refs; listen; history; text; internal format)
 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: A016465 A122947 A231147 * A224489 A318933 A140334 Adjacent sequences:  A046531 A046532 A046533 * A046535 A046536 A046537 KEYWORD tabf,nonn,easy AUTHOR STATUS approved

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Last modified June 20 21:35 EDT 2021. Contains 345255 sequences. (Running on oeis4.)