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A160860 The least possible number of pieces resulting from cutting a convex n-gon along all its diagonals. 3
1, 4, 11, 24, 47, 80 (list; graph; refs; listen; history; text; internal format)
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: A167875 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

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Last modified December 17 14:12 EST 2018. Contains 318201 sequences. (Running on oeis4.)