A230503 Irregular triangle read by rows: possible number of interior intersection points of the diagonals of an n-sided convex polygon.

0, 1, 5, 13, 15, 29, 31, 33, 35, 49, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 70

Offset

3,3

Comments

Beginning from number of sides equal to 12 the terms no longer increase between rows. For example, the number of inner diagonal intersection points for the regular 12-gon is fewer than the number of inner diagonal intersection points for regular 11-gon.

Obviously there exists a number k_0 such that k_0 is not in the sequence and k is in the sequence for all k > k_0.

Links

Table of n, a(n) for n=3..28.

Vladimir Letsko, Mathematical Marathon at vspu, Problem 102 (in Russian)

Vladimir Letsko Illustration of all cases for number of sides from 3 to 8

V. A. Letsko and M. A. Voronina Classification of convex polygons, Grani Poznaniya, 1(11), 2011 (in Russian).

Example

The beginning of the irregular triangle is:
3| 0
4| 1
5| 5
6| 13, 15
7| 29, 31, 33, 35
8| 49, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 70

Crossrefs

Cf. A006561, A230281, A000332, A230150.

Sequence in context: A309812 A324909 A322105 * A335695 A067696 A050598

Adjacent sequences: A230500 A230501 A230502 * A230504 A230505 A230506

Keyword

tabf,more,nonn

Author

Vladimir Letsko, Oct 21 2013

Status

approved