%I #32 Dec 08 2017 17:43:54

%S 1,4,11,24,47,80

%N The least possible number of pieces resulting from cutting a convex n-gon along all its diagonals.

%C It seems that a(9)=137 and a(n) = A007678(n) for all even n.

%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 Vladimir Letsko, <a href="/A160860/a160860.pdf">Illustration of all cases for number of sides from 3 to 8</a> [Cached copy, pdf version only]

%H Vladimir Letsko, <a href="http://www-old.fizmat.vspu.ru/doku.php?id=marathon:problem_102">Proof for n = 7 and n = 8 and example for n = 9</a> (in Russian)

%H Vladimir Letsko, <a href="/A160860/a160860_1.pdf">Proof for n = 7 and n = 8 and example for n = 9</a> (in Russian). [Cached copy, pdf version only]

%H V. A. Letsko, 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)

%H B. Poonen and M. Rubinstein, <a href="http://arXiv.org/abs/math.MG/9508209">The number of intersection points made by the diagonals of a regular polygon</a>.

%Y Cf. A006522, A007678, A230281.

%K hard,more,nonn,nice

%O 3,2

%A _Vladimir Letsko_, May 29 2009, May 30 2009, Apr 20 2010