A067153 Number of hexagonal regions in regular n-gon with all diagonals drawn.

0, 0, 0, 9, 0, 22, 0, 39, 0, 105, 48, 136, 18, 190, 120, 462, 66, 644, 72, 875, 390, 1296, 952, 1595, 450, 1891, 1472, 3201, 2346, 3640, 2124, 4773, 2698, 5577, 4000, 7298, 3444, 7912, 6336, 10980, 6532, 10904, 7824, 14651, 12150, 16779, 13260, 20299, 13176, 21560, 18200, 26961, 21634, 29500

Offset

6,4

References

B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Links

Scott R. Shannon, Table of n, a(n) for n = 6..765

Sascha Kurz, m-gons in regular n-gons

B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, SIAM J. on Discrete Mathematics, Vol. 11, No. 1, 135-156 (1998).

Sequences formed by drawing all diagonals in regular polygon

Example

a(9)=9 because drawing the regular 9-gon with all its diagonals yields 9 hexagons.

Crossrefs

Cf. A007678, A067165, A064869, A067151, A067152, A067154, A067155, A067156, A067157, A067158, A067159.

Sequence in context: A299154 A070929 A007394 * A057405 A167354 A005066

Adjacent sequences: A067150 A067151 A067152 * A067154 A067155 A067156

Keyword

nonn

Author

Sascha Kurz, Jan 06 2002

Extensions

a(54) and beyond from Scott R. Shannon, Dec 04 2021

Definition clarified by N. J. A. Sloane, Jun 09 2025

Status

approved