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A194305
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Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= n, 1 <= k <= n.
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3
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1, 2, 0, 2, 1, 0, 1, 2, 1, 0, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 2, 1, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 2, 1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 0, 2, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2
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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 eleven rows:
1;
2, 0;
2, 1, 0;
1, 2, 1, 0;
1, 1, 2, 1, 0;
1, 1, 1, 1, 1, 1;
1, 1, 1, 1, 1, 1, 1;
0, 2, 1, 1, 1, 1, 1, 1;
0, 2, 2, 1, 0, 1, 1, 1, 1;
0, 2, 2, 0, 2, 1, 0, 1, 1, 1;
0, 2, 0, 2, 2, 0, 2, 1, 0, 1, 1;
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MATHEMATICA
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r = Pi;
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}]
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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