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A194293
Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n, r=(1+sqrt(5))/2, the golden ratio.
3
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,26
COMMENTS
See A194285. Which rows are constant?
EXAMPLE
First ten rows:
1
1..1
1..1..1
1..1..1..1
1..1..1..1..1
1..1..1..1..1..1
1..1..1..1..2..1..0
1..1..1..1..1..1..1..1
1..0..2..0..1..2..1..1..1
1..1..1..1..1..1..1..1..1..1
MATHEMATICA
r = GoldenRatio;
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[%] (* A194293 *)
CROSSREFS
Cf. A194293.
Sequence in context: A073484 A203947 A081396 * A349595 A298941 A317146
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 21 2011
STATUS
approved