

A194335


Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=2tau, where tau=(1+sqrt(5))/2, the golden ratio.


2



1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 5, 4, 5, 6, 7, 5, 7, 6, 6, 7, 8, 7, 6, 8, 7, 8, 8, 8, 9, 7, 8, 8, 8, 8, 10, 8, 10, 9, 9, 9, 9, 9, 10, 10, 11, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 11, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13
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OFFSET

1,2


COMMENTS

See A194285.


LINKS

Table of n, a(n) for n=1..81.


EXAMPLE

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


MATHEMATICA

r = 2GoldenRatio;
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[%] (* A194335 *)


CROSSREFS

Cf. A194285.
Sequence in context: A056155 A157684 A194339 * A026099 A049727 A260690
Adjacent sequences: A194332 A194333 A194334 * A194336 A194337 A194338


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 22 2011


STATUS

approved



