A363979 Number of nonsimilar polygonal regions in a regular n-gon with all diagonals drawn.

1, 1, 3, 3, 7, 7, 14, 13, 25, 19, 37, 35, 58, 53, 82, 58, 112, 98, 150, 133, 177, 151, 239, 212, 300, 275, 369, 244, 455, 409, 530, 488, 631, 526, 736, 683, 858, 800, 975, 794, 1133, 1056, 1291, 1227, 1487, 1289, 1666, 1600, 1889, 1797, 2102, 1884, 2373, 2242, 2621, 2496, 2878, 2458

Offset: 3

Author

Christopher Scussel, Jun 30 2023

Keywords

• nonn

Comments

Alternatively, the number of equivalence classes of an equivalence relation on the polygonal regions in a regular n-gon with all diagonals drawn, where two regions are equivalent iff they are similar.

Examples

			This sequence is the same as A187781 for n<10 because n=10 is the smallest n such that there exist regions that are similar but not congruent.
		

Links

• Bjorn Poonen and Michael Rubinstein, The Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics 11 (1998), nr. 1, pp. 135-156; doi: 10.1137/S0895480195281246; arXiv version, arXiv:math/9508209 [math.MG], 1995-2006.
• Christopher Scussel, Illustration of similarity without congruence at a(10)

Crossrefs

Cf. A187781, A007678.