A288180 Number of intersection points formed by drawing the line segments connecting any two lattice points of an n X m convex lattice polygon written as triangle T(n,m), n >= 1, 1 <= m <= n.

5, 13, 37, 35, 121, 353, 75, 265, 771, 1761, 159, 587, 1755, 4039, 8917, 275, 1019, 3075, 7035, 15419, 26773, 477, 1797, 5469, 12495, 27229, 47685, 84497, 755, 2823, 8693, 19831, 43333, 76357, 135075, 215545, 1163, 4369, 13301, 30333, 66699, 117719, 207643, 331233, 508613

Offset

1,1

Comments

If more than two lines intersect in the same point, only one intersection is counted.

References

For references and links see A288177.

Links

Lars Blomberg, Table of n, a(n) for n = 1..325 (The first 25 rows)

Lars Blomberg, Scott R. Shannon, N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids, (2021). Also arXiv:2009.07918.

Hugo Pfoertner, Illustrations of Chamber Complexes up to 5 X 5.

Hugo Pfoertner, Illustration of intersection points up to 6 X 6.

Index entries for sequences related to stained glass windows

Example

Triangle starts with:
n=1: 5,
n=2: 13, 37,
n=3: 35, 121, 353,
n=4: 75, 265, 771, 1761,
n=5: 159, 587, 1755, 4039, 8917,
n=6: 275, 1019, 3075, 7035, 15419, 26773,
n=7: 477, 1797, 5469, 12495, 27229, 47685, 84497,
n=8: 755, 2823, 8693, 19831, 43333, 76357, 135075, 215545,
n=9: 1163, 4369, 13301, 30333, 66699, 117719, 207643, 331233, 508613,
...

Crossrefs

Cf. A288177, A288187.

For column 2 see A333279, A333280, A333281.

The main diagonal T(n,n) is A343993.

Sequence in context: A266102 A332599 A331453 * A333284 A141408 A238460

Adjacent sequences: A288177 A288178 A288179 * A288181 A288182 A288183

Keyword

nonn,tabl

Author

Hugo Pfoertner, Jun 06 2017

Extensions

Corrected and extended by Hugo Pfoertner, Jul 20 2017

Status

approved