A194315 Triangular array: g(n,k)=number of fractional parts (i*sqrt(6)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.

1, 2, 2, 3, 3, 3, 4, 5, 3, 4, 4, 6, 5, 5, 5, 5, 6, 8, 4, 7, 6, 7, 7, 6, 7, 8, 7, 7, 6, 9, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 11, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 14, 10, 12, 13, 12, 12, 12, 13, 13, 12

Offset: 1

Author

Clark Kimberling, Aug 21 2011

Keywords

• nonn
• tabl

Comments

See A194285.

Examples

			First eight rows:
1
2..2
3..3..3
4..5..3..4
4..6..5..5..5
5..6..8..4..7..6
7..7..6..7..8..7..7
6..9..8..9..7..8..8..9
		

Crossrefs

Cf. A194315.

Programs

Mathematica

r = Sqrt[6];
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^2}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194315 *)