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

1,1

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.

Sequence in context: A362501 A233290 A167245 * A205087 A064182 A139792

Adjacent sequences: A331926 A331927 A331928 * A331930 A331931 A331932

Keyword

nonn

Author

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

Extensions

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

Status

approved