

A194307


Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k1)/n, k/n], for 1 <= i <= n^2, 1 <= k <= n.


2



1, 3, 1, 4, 2, 3, 3, 5, 4, 4, 4, 5, 7, 3, 6, 6, 5, 5, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 8, 9, 9, 9, 8, 9, 8, 11, 10, 8, 7, 9, 11, 10, 10, 10, 11, 9, 9, 12, 9, 9, 11, 10, 12, 10, 12, 11, 10, 11, 12, 10, 11, 12, 9, 14, 11, 13, 14, 10, 13, 10, 13, 12, 11, 14, 8, 17, 11, 14
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

See A194285.


LINKS

Table of n, a(n) for n=1..82.


EXAMPLE

First eight rows:
1;
3, 1;
4, 2, 3;
3, 5, 4, 4;
4, 5, 7, 3, 6;
6, 5, 5, 5, 8, 7;
7, 7, 7, 7, 7, 7, 7;
8, 7, 7, 7, 8, 9, 9, 9;


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^2}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%] (* A194307 *)


CROSSREFS

Cf. A194285.
Sequence in context: A242111 A209919 A116537 * A048225 A155481 A075148
Adjacent sequences: A194304 A194305 A194306 * A194308 A194309 A194310


KEYWORD

nonn,tabl,changed


AUTHOR

Clark Kimberling, Aug 21 2011


STATUS

approved



