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A194301
Triangular array: g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n.
2
1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 1, 1, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 2, 0, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 2, 0, 1, 1, 0, 1, 2, 0, 2, 1, 0, 2, 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
OFFSET
1,2
COMMENTS
See A194285.
EXAMPLE
First nine rows:
1
2..0
1..1..1
1..1..1..1
1..1..1..1..1
0..2..2..0..1..1
0..2..1..1..2..0..1
0..2..0..2..0..2..0..2
0..2..1..1..1..1..1..1..1
MATHEMATICA
r = Sqrt[5];
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[%] (* A194301 *)
CROSSREFS
Cf. A194285.
Sequence in context: A154782 A265196 A171157 * A194341 A171905 A327406
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 21 2011
STATUS
approved