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EXAMPLE
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F(1) = (0/1, 1/1) -> (0+1=1, 1+1=2).
F(2) = (0/1, 1/2, 1/1) -> (0+1=1, 1+2=3, 1+1=2).
F(3) = (0/1, 1/3, 1/2, 2/3, 1/1) -> (0+1=1, 1+3=4, 1+2=3, 2+3=5, 1+1=2).
F(4) = (0/1, 1/4, 1/3, 1/2, 2/3, 3/4, 1/1) -> (0+1=1, 1+4=5, 1+3=4, 1+2=3, 2+3=5, 3+4=7, 1+1=2).
The 5th row is formed from the 5th row of the table of Farey fractions:
F(5) = (0/1, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1) whose sum of numerators and denominators is (1, 6, 5, 4, 7, 3, 8, 5, 7, 9, 2).
F(6) = (0/1, 1/6, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 1/1} whose sums are (1, 7, 6, 5, 4, 7, 3, 8, 5, 7, 9, 11, 2).
F(7) = (0/1, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 2/5, 3/7, 1/2, 4/7, 3/5, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 1/1) whose sums are (1, 8, 7, 6, 5, 9, 4, 7, 10, 3, 11, 8, 5, 12, 7, 9, 11, 13, 2).
F(8) = (0/1, 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8, 1/1) whose sums are (1, 9, 8, 7, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 11, 13, 15, 2).
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