A194306 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

LINKS

Table of n, a(n) for n=1..100.

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

Sequence in context: A214640 A224965 A194298 * A283325 A353707 A318438

Adjacent sequences: A194303 A194304 A194305 * A194307 A194308 A194309

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 21 2011

STATUS

approved