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

0,5

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.

Links

Table of n, a(n) for n=0..76.

Formula

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

Example

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.

Sequence in context: A195425 A131701 A021688 * A290823 A370706 A090642

Adjacent sequences: A119436 A119437 A119438 * A119440 A119441 A119442

Keyword

nonn,tabl

Author

Franklin T. Adams-Watters, May 19 2006

Status

approved