A194324 Triangular array: g(n,k)=number of fractional parts (i*sqrt(1/2)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 6, 6, 6, 8, 6, 11, 10, 11, 11, 11, 10, 19, 18, 18, 19, 18, 19, 17, 33, 32, 31, 32, 32, 32, 32, 32, 56, 58, 57, 57, 57, 56, 57, 56, 58, 103, 102, 102, 103, 102, 102, 103, 103, 102, 102, 186, 186, 188, 184, 188, 186, 185, 187, 186, 186

Offset: 1

Author

Clark Kimberling, Aug 22 2011

Keywords

• nonn
• tabl

Comments

See A194285.

Examples

			First eight rows:
2
2...2
2...3...3
4...4...4...4
6...6...6...8...6
11..10..11..11..11..10
19..18..18..19..18..19..17
33..32..31..32..32..32..32..32
		

Crossrefs

Cf. A194285.

Programs

Mathematica

r = Sqrt[1/2];
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, 2^n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194324 *)