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

Author

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

Keywords

• nonn

Comments

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

Links

• 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.

Extensions

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