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A194305 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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194285.

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

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;

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: A186809 A112300 A049239 * A036580 A101674 A100820

Adjacent sequences:  A194302 A194303 A194304 * A194306 A194307 A194308

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 21 2011

STATUS

approved

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Last modified June 14 00:35 EDT 2021. Contains 345016 sequences. (Running on oeis4.)