A119439 Triangle T(n,k) = number of sets of m points determined by the intersection of a line with an n X n grid of points.

1, 1, 1, 1, 4, 6, 1, 9, 12, 8, 1, 16, 48, 4, 10, 1, 25, 108, 16, 4, 12, 1, 36, 248, 36, 4, 4, 14, 1, 49, 428, 64, 20, 4, 4, 16, 1, 64, 764, 100, 44, 4, 4, 4, 18, 1, 81, 1196, 204, 36, 24, 4, 4, 4, 20, 1, 100, 1900, 252, 64, 52, 4, 4, 4, 4, 22, 1, 121, 2668, 396, 124, 40, 28, 4, 4, 4, 4

Offset: 0

Author

Franklin T. Adams-Watters, May 19 2006

Keywords

• nonn
• tabl

Comments

Each singleton point is determined by all but finitely many of the family of lines passing through that point and the empty set is determined by any randomly positioned line.

Examples

			The table starts:
1,
1,1,
1,4,6,
1,9,12,8,
1,16,48,4,10,
		

Crossrefs

Row sums A119438; columns A000290, A018809-A018817. See A119437 for another version.

Formula

T(n,0) = 1, T(n,1) = n^2, T(n,k) = A119437(n,k) for k>1.