A194312 Triangular array: g(n,k)=number of fractional parts (i*e) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

2, 2, 2, 3, 2, 3, 4, 5, 4, 3, 6, 7, 6, 6, 7, 10, 11, 11, 11, 11, 10, 18, 18, 18, 18, 18, 19, 19, 32, 32, 31, 32, 32, 33, 32, 32, 57, 58, 56, 57, 57, 56, 59, 56, 56, 104, 102, 101, 103, 103, 102, 102, 103, 102, 102, 187, 186, 186, 186, 187, 185, 187, 186, 186, 187

Offset: 1

Author

Clark Kimberling, Aug 21 2011

Keywords

• nonn
• tabl

Comments

See A194285.

Examples

			First eight rows:
2
2...2
3...2...3
4...5...4...3
6...7...6...6...7
10..11..11..11..11..10
18..18..18..18..18..19..19
32..32..31..32..32..33..32..32
		

Crossrefs

Cf. A194285.

Programs

Mathematica

r = E;
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[%]    (* A194312 *)