A288180 - OEIS

%I #38 May 21 2021 07:09:07

%S 5,13,37,35,121,353,75,265,771,1761,159,587,1755,4039,8917,275,1019,

%T 3075,7035,15419,26773,477,1797,5469,12495,27229,47685,84497,755,2823,

%U 8693,19831,43333,76357,135075,215545,1163,4369,13301,30333,66699,117719,207643,331233,508613

%N 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.

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

%D For references and links see A288177.

%H Lars Blomberg, <a href="/A288180/b288180.txt">Table of n, a(n) for n = 1..325</a> (The first 25 rows)

%H Lars Blomberg, Scott R. Shannon, N. J. A. Sloane, <a href="http://neilsloane.com/doc/rose_5.pdf">Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids</a>, (2021). Also arXiv:2009.07918.

%H Hugo Pfoertner, <a href="/A288177/a288177.pdf">Illustrations of Chamber Complexes up to 5 X 5</a>.

%H Hugo Pfoertner, <a href="/A288180/a288180_1.pdf">Illustration of intersection points up to 6 X 6</a>.

%H <a href="/index/St#Stained">Index entries for sequences related to stained glass windows</a>

%e Triangle starts with:

%e n=1: 5,

%e n=2: 13, 37,

%e n=3: 35, 121, 353,

%e n=4: 75, 265, 771, 1761,

%e n=5: 159, 587, 1755, 4039, 8917,

%e n=6: 275, 1019, 3075, 7035, 15419, 26773,

%e n=7: 477, 1797, 5469, 12495, 27229, 47685, 84497,

%e n=8: 755, 2823, 8693, 19831, 43333, 76357, 135075, 215545,

%e n=9: 1163, 4369, 13301, 30333, 66699, 117719, 207643, 331233, 508613,

%e ...

%Y Cf. A288177, A288187.

%Y For column 2 see A333279, A333280, A333281.

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

%K nonn,tabl

%O 1,1

%A _Hugo Pfoertner_, Jun 06 2017

%E Corrected and extended by _Hugo Pfoertner_, Jul 20 2017