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A288180
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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.
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7
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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
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OFFSET
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1,1
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COMMENTS
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If more than two lines intersect in the same point, only one intersection is counted.
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REFERENCES
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For references and links see A288177.
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LINKS
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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
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EXAMPLE
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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,
...
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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Hugo Pfoertner, Jun 06 2017
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EXTENSIONS
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Corrected and extended by Hugo Pfoertner, Jul 20 2017
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STATUS
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approved
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