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A194291
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Triangular array: g(n,k)=number of fractional parts (i*sqrt(3)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.
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2
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1, 2, 2, 2, 4, 3, 4, 3, 5, 4, 5, 5, 5, 5, 5, 5, 6, 7, 6, 5, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7, 9, 7, 9, 8, 8, 8, 9, 9, 9, 9, 10, 8, 9, 10, 10, 10, 10, 10, 11, 9, 10, 11, 9, 10, 10, 11, 11, 10, 12, 11, 11, 12, 11, 11, 11, 11, 12, 13, 11, 12, 13, 12, 11, 13, 12, 11, 13, 13, 13, 13
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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First eight rows:
1
2..2
2..4..3
4..3..5..4
5..5..5..5..5
5..6..7..6..5..7
7..7..7..7..7..7..7
8..8..7..9..7..9..8..8
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MATHEMATICA
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r = Sqrt[3];
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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