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

3,2

Comments

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

Links

Table of n, a(n) for n=3..8.

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.

Sequence in context: A006527 A057304 A001752 * A192748 A143075 A290707

Adjacent sequences: A160857 A160858 A160859 * A160861 A160862 A160863

Keyword

hard,more,nonn,nice

Author

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

Status

approved