A355838 Number of regions formed in a square by straight line segments when connecting the n+1 points along each edge that divide it into n equal parts to the n+1 points on the edge on the opposite side of the square.

4, 40, 184, 496, 1240, 2144, 4380, 6720, 10860, 15528, 24300, 30152, 46036, 57496, 75056, 96416, 129052, 148512, 198392, 225240, 279576, 336272, 415988, 453376, 565052, 648008, 754808, 848664, 1026040, 1085536, 1331532, 1452704, 1652684, 1862600, 2084888, 2247568, 2662092, 2887944, 3193744

Offset: 1

Author

Scott R. Shannon, Jul 18 2022

Keywords

• nonn

Comments

This sequence is similar to A355798 but here the corner vertices of the square are also connected to points on the opposite edge.

Links

• Scott R. Shannon, Image for n = 2.
• Scott R. Shannon, Image for n = 3.
• Scott R. Shannon, Image for n = 4.
• Scott R. Shannon, Image for n = 5.
• Scott R. Shannon, Image for n = 6.
• Scott R. Shannon, Image for n = 7.
• Scott R. Shannon, Image for n = 8.
• Scott R. Shannon, Image for n = 11.
• Scott R. Shannon, Image for n = 16.

Crossrefs

Cf. A355839 (vertices), A355840 (edges), A355841 (k-gons), A355798 (without corner vertices), A290131, A331452, A335678.

Formula

a(n) = A355840(n) - A355839(n) + 1 by Euler's formula.