A331906 The number of regions inside a pentagram formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

40, 1100, 7330, 25540, 65930, 136200, 263010, 458410, 740550, 1142740, 1681640, 2400970, 3338850, 4495510, 5962220, 7736150, 9924580, 12442880, 15527670, 19132140, 23301600, 28070620, 33585800, 39919140, 47157510, 55209750, 64185300, 74311940, 85731780, 98167130

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..30.

Scott R. Shannon, Pentagram regions for n = 1.

Scott R. Shannon, Pentagram regions for n = 2.

Scott R. Shannon, Pentagram regions for n = 3.

Scott R. Shannon, Pentagram regions for n = 4.

Scott R. Shannon, Pentagram regions for n = 5.

Scott R. Shannon, Pentagram regions for n = 6.

Scott R. Shannon, Pentagram regions with random distance-based coloring for n = 1.

Scott R. Shannon, Pentagram regions with random distance-based coloring for n = 2.

Scott R. Shannon, Pentagram regions with random distance-based coloring for n = 3.

Scott R. Shannon, Pentagram regions with random distance-based coloring for n = 4.

Scott R. Shannon, Pentagram regions with random distance-based coloring for n = 5.

Eric Weisstein's World of Mathematics, Pentagram.

Crossrefs

Cf. A331907 (n-gons), A333117 (vertices), A333118 (edges), A007678, A092867, A331452.

Sequence in context: A284838 A124100 A071952 * A144914 A004385 A349596

Adjacent sequences: A331903 A331904 A331905 * A331907 A331908 A331909

Keyword

nonn

Author

Scott R. Shannon and N. J. A. Sloane, Jan 31 2020

Extensions

a(7)-a(30) from Lars Blomberg, May 06 2020

Status

approved