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A194294
Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=2n, r=(1+sqrt(5))/2, the golden ratio.
2
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 3, 1, 3, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 1, 2, 3, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2
OFFSET
1,1
COMMENTS
See A194285.
EXAMPLE
First nine rows:
2
2..2
2..2..2
2..2..2..2
2..2..2..2..2
1..3..2..2..2..2
2..2..2..2..3..2..1
2..2..2..2..2..2..2..2
2..2..3..1..2..3..1..3..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, 2n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%] (* A194294 *)
CROSSREFS
Sequence in context: A044926 A074264 A194302 * A263110 A044927 A343643
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 21 2011
STATUS
approved