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

5,3

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

Example

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

Crossrefs

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

Sequence in context: A348516 A245543 A225949 * A052440 A246919 A167299

Adjacent sequences: A067149 A067150 A067151 * A067153 A067154 A067155

Keyword

nonn

Author

Sascha Kurz, Jan 06 2002

Extensions

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

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

Status

approved