A194286 Triangular array: g(n,k)=number of fractional parts (i*sqrt(2)) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n.

2, 2, 2, 2, 3, 1, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 1, 3, 2, 1, 3, 1, 3, 1, 3, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 1, 3, 2, 3, 1, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 1, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Clark Kimberling, Aug 21 2011

Keywords

• nonn
• tabl

Comments

See A194285.

Examples

			First eight rows:
2
2..2
2..3..1
2..3..1..2
2..2..2..2..2
2..2..2..2..2..2
2..1..3..2..1..3..2
1..3..1..3..1..3..2..2
		

Crossrefs

Cf. A194285.

Programs

Mathematica

r = Sqrt[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[%]    (* A194286 *)