A331929 The number of regions inside a pentagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

11, 170, 1161, 3900, 10741, 22380, 44491, 76610, 126336, 194070, 290651, 410860, 577721, 779340, 1035676, 1345030, 1730696, 2176040, 2724036, 3345880, 4087656, 4933200, 5921991, 7018210, 8300896, 9723300, 11339151, 13122120, 15150271, 17345140, 19843056

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Feb 01 2020

Keywords

• nonn

Comments

The terms are from numeric computation - no formula for a(n) is currently known.

Links

• Lars Blomberg, Table of n, a(n) for n = 1..35
• Scott R. Shannon, Pentagon regions for n = 1.
• Scott R. Shannon, Pentagon regions for n = 2.
• Scott R. Shannon, Pentagon regions for n = 3.
• Scott R. Shannon, Pentagon regions for n = 4.
• Scott R. Shannon, Pentagon regions for n = 5.
• Scott R. Shannon, Pentagon regions for n = 6.
• Scott R. Shannon, Pentagon regions for n = 7.
• Scott R. Shannon, Pentagon regions for n = 8.
• Scott R. Shannon, Pentagon regions for n = 5, random distance-based coloring.
• Scott R. Shannon, Pentagon regions for n = 6, random distance-based coloring
• Wikipedia, Pentagon.

Crossrefs

Cf. A331939 (n-gons), A329710 (edges), A330847 (vertices), A007678, A092867, A331452, A331931.

Extensions

a(9) and beyond from Lars Blomberg, May 11 2020