A194331 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=2-sqrt(3).

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

Offset: 1

Author

Clark Kimberling, Aug 22 2011

Keywords

• nonn
• tabl

Comments

See A194285.

Examples

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

Crossrefs

Cf. A194285.

Programs

Mathematica

r = 2-Sqrt[3];
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[%]    (* A194331 *)