login
A194298
Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n, r=(1+sqrt(3))/2.
2
2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 1, 3, 1, 3, 2, 1, 3, 1, 3, 1, 2, 3, 1, 2, 3, 1, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2
OFFSET
1,1
COMMENTS
See A194285.
EXAMPLE
First eight rows:
2
3..1
2..2..2
2..2..2..2
2..2..2..2..2
2..2..3..2..2..1
3..1..3..2..1..3..1
3..1..2..3..1..2..3..1
MATHEMATICA
r = (1+Sqrt[3])/2;
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[%] (* A194298 *)
CROSSREFS
Cf. A194298.
Sequence in context: A106798 A214640 A224965 * A194306 A283325 A353707
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 21 2011
STATUS
approved