A194319 Triangular array: g(n,k)=number of fractional parts (i*sqrt(8)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.

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

Offset: 1

Author

Clark Kimberling, Aug 22 2011

Keywords

• nonn
• tabl

Comments

See A194285.

Examples

			First nine rows:
1
2...2
2...4...3
2...6...3...5
4...5...5...6...5
6...5...6...6...7...6
7...6...6...7...8...8...7
8...8...8...8...8...8...7...9
8...9...10..7...10..10..8...10...9
		

Crossrefs

Cf. A194285.

Programs

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^2}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194319 *)