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A194306
Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= 2n, 1 <= k <= n.
1
2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 0, 3, 3, 3, 1, 2, 2, 2, 2, 0, 3, 3, 0, 3, 3, 2, 1, 3, 2, 0, 4, 1, 2, 3, 0, 3, 3, 0, 3, 3, 0, 4, 0, 4, 3, 1, 3, 0, 3, 1, 2, 3, 0, 4, 0, 4, 0, 4, 0, 4, 2, 2, 2, 1, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0
OFFSET
1,1
COMMENTS
See A194285.
EXAMPLE
First nine rows:
3;
3, 1;
2, 2, 2;
2, 2, 2, 2;
2, 2, 3, 1, 2;
2, 2, 2, 2, 2, 2;
2, 2, 2, 2, 2, 2, 2;
1, 2, 3, 2, 2, 2, 2, 2;
0, 3, 3, 3, 1, 2, 2, 2, 2;
MATHEMATICA
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}]]
Flatten[%] (* A194305 *)
CROSSREFS
Cf. A194285.
Sequence in context: A214640 A224965 A194298 * A283325 A353707 A318438
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 21 2011
STATUS
approved