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A194317
Triangular array: g(n,k)=number of fractional parts (i*sqrt(8)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n.
2
1, 0, 2, 0, 2, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 0, 1, 1, 1, 0, 2, 2, 1, 0, 1, 1, 0, 2, 2, 0, 2, 1, 0, 1, 1, 1, 2, 0, 2, 1, 1, 1, 0, 2, 0, 2, 0, 2, 1, 1, 1, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1, 1, 1, 1, 0, 2, 0, 3, 0, 2, 0, 2, 0, 1, 1, 0, 2, 0
OFFSET
1,3
COMMENTS
See A194285.
EXAMPLE
First eight rows:
1
0..2
0..2..1
0..2..1..1
1..1..1..1..1
1..1..1..1..1..1
1..0..1..1..1..2..1
0..1..1..1..0..2..2..1
MATHEMATICA
r = Sqrt[8];
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[%] (* A194317 *)
CROSSREFS
Cf. A194285.
Sequence in context: A321101 A067167 A255195 * A096810 A190436 A133696
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 22 2011
STATUS
approved