A160860 The least possible number of pieces resulting from cutting a convex n-gon along all its diagonals.

1, 4, 11, 24, 47, 80

Offset: 3

Author

Vladimir Letsko, May 29 2009, May 30 2009, Apr 20 2010

Keywords

• hard
• more
• nonn
• nice

Comments

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

Links

• Vladimir Letsko, Illustration of all cases for number of sides from 3 to 8
• Vladimir Letsko, Illustration of all cases for number of sides from 3 to 8 [Cached copy, pdf version only]
• Vladimir Letsko, Proof for n = 7 and n = 8 and example for n = 9 (in Russian)
• Vladimir Letsko, Proof for n = 7 and n = 8 and example for n = 9 (in Russian). [Cached copy, pdf version only]
• V. A. Letsko, M. A. Voronina, Classification of convex polygons, Grani Poznaniya, 1(11), 2011. (in Russian)
• B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon.

Crossrefs

Cf. A006522, A007678, A230281.