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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.

%I A046213 #23 Mar 31 2017 22:35:47
%S A046213 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,
%T A046213 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,
%U A046213 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
%N 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.
%H A046213 Peter J. C. Moses, <a href="/A046213/b046213.txt">Table of n, a(n) for n = 1..10000</a>
%e A046213 1/1;
%e A046213 1/1  1/1;
%e A046213 1/1  1/2  1/1;
%e A046213 1/1  3/2  3/2  1/1;
%e A046213 1/1  5/2  3/1  5/2  1/1;
%e A046213 1/1  7/2 11/2 11/2  7/2  1/1;
%e A046213 1/1  9/2  9/1 11/1  9/1  9/2  1/1;
%e A046213 1/1 11/2 27/2 20/1 20/1 27/2 11/2 1/1; ...
%t A046213 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 *)
%K A046213 nonn,tabf,less
%O A046213 1,10
%A A046213 _Mohammad K. Azarian_