A067152 Number of pentagonal regions in regular n-gon with all diagonals drawn.

1, 0, 7, 0, 18, 10, 44, 0, 117, 98, 150, 128, 357, 72, 646, 580, 903, 814, 1564, 840, 2050, 2106, 2862, 2128, 3625, 1440, 5146, 4896, 6105, 5542, 8190, 7452, 10471, 10184, 14235, 13160, 16564, 11382, 21156, 20548, 24300, 23920, 30362, 26112, 35231, 32700, 40341, 38532, 51834, 42012, 58905

Offset: 5

Author

Sascha Kurz, Jan 06 2002

Keywords

• nonn

Examples

			a(5) = 1 because only the center-region is a pentagon.
		

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 = 5..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

Crossrefs

Cf. A007678, A067164, A064869, A067151, A067153, A067154, A067155, A067156, A067157, A067158, A067159.

Extensions

a(49) and beyond from Scott R. Shannon, Dec 04 2021

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