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
Examples
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, ...
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
Crossrefs
Extensions
Corrected and extended by Hugo Pfoertner, Jul 20 2017
Comments