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

1,1

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

Table of n, a(n) for n=1..39.

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.

Formula

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

Crossrefs

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

Sequence in context: A163322 A238328 A009355 * A061132 A215717 A270099

Adjacent sequences: A355835 A355836 A355837 * A355839 A355840 A355841

Keyword

nonn

Author

Scott R. Shannon, Jul 18 2022

Status

approved