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A049805
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Triangular array T read by rows: T(n,k) is the number of Farey fractions of order n that are <= 1/k for k=1..n, for n>=1.
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11
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2, 3, 2, 5, 3, 2, 7, 4, 3, 2, 11, 6, 4, 3, 2, 13, 7, 5, 4, 3, 2, 19, 10, 7, 5, 4, 3, 2, 23, 12, 8, 6, 5, 4, 3, 2, 29, 15, 10, 8, 6, 5, 4, 3, 2, 33, 17, 12, 9, 7, 6, 5, 4, 3, 2, 43, 22, 15, 11, 9, 7, 6, 5, 4, 3, 2, 47, 24, 16, 12, 10, 8, 7, 6, 5, 4, 3, 2
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OFFSET
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1,1
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COMMENTS
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So, T(n, k) is also the index of fraction 1/k in the Farey fractions of order n. - Michel Marcus, Jun 27 2014
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LINKS
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Table of n, a(n) for n=1..78.
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EXAMPLE
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Rows: {2}; {3,2}; {5,3,2}; ...; e.g. in row 3, 5 reduced fractions (0/1,1/3,1/2,2/3,1/1) are <=1; 3 are <=1/2; 2 are <=1/3.
Triangle starts:
2;
3, 2;
5, 3, 2;
7, 4, 3, 2;
11, 6, 4, 3, 2;
13, 7, 5, 4, 3, 2;
...
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MATHEMATICA
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T[n_, k_] := Count[FareySequence[n], f_ /; f <= 1/k];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 25 2018 *)
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PROG
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(PARI) row(nn) = my(frow = farey(n)); for (k=1, n, print1(vecsearch(frow, 1/k), ", "); ); \\ Michel Marcus, Jun 27 2014
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CROSSREFS
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First column: T(n, 1) = A005728(n+1).
Cf. A006842, A006843.
Sequence in context: A108728 A331962 A302170 * A104887 A064886 A029600
Adjacent sequences: A049802 A049803 A049804 * A049806 A049807 A049808
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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