A194295 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n^2, r=(1+sqrt(5))/2, the golden ratio.

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

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..4..4..4
4..5..6..5..5
6..7..5..7..6..5
7..8..6..7..8..7..6
8..8..8..7..9..8..8..8
		

Crossrefs

Cf. A194295.

Programs

Mathematica

r = GoldenRatio;
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[%]    (* A194295 *)