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%I #13 Oct 22 2013 16:25:02
%S 0,1,5,13,15,29,31,33,35,49,52,53,54,56,57,58,59,60,61,62,63,64,65,66,
%T 68,70
%N Irregular triangle read by rows: possible number of interior intersection points of the diagonals of an n-sided convex polygon.
%C 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.
%C 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.
%H Vladimir Letsko, <a href="http://www-old.fizmat.vspu.ru/doku.php?id=marathon:problem_102">Mathematical Marathon at vspu, Problem 102</a> (in Russian)
%H Vladimir Letsko <a href="http://www-old.fizmat.vspu.ru/doku.php?id=marathon:illustrations_102_co">Illustration of all cases for number of sides from 3 to 8</a>
%H V. A. Letsko and M. A. Voronina <a href="http://grani.vspu.ru/files/publics/1301378772.pdf">Classification of convex polygons</a>, Grani Poznaniya, 1(11), 2011 (in Russian).
%e The beginning of the irregular triangle is:
%e 3| 0
%e 4| 1
%e 5| 5
%e 6| 13, 15
%e 7| 29, 31, 33, 35
%e 8| 49, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 70
%Y Cf. A006561, A230281, A000332, A230150.
%K tabf,more,nonn
%O 3,3
%A _Vladimir Letsko_, Oct 21 2013
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