

A355798


Number of regions formed in a square by straight line segments when connecting the n1 points between each corner that divide each edge into n equal parts to the n1 points on the edge on the opposite side of the square.


13



1, 4, 24, 104, 316, 712, 1588, 2816, 4940, 7672, 12444, 16840, 25968, 34088, 46260, 61048, 82792, 98984, 133032, 156072, 196236, 239048, 298292, 334032, 417072, 483856, 570200, 649816, 786412, 850000, 1037628, 1145424, 1311536, 1485880, 1677660, 1828360, 2158192, 2357376, 2623604, 2852688
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..40.
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 = 16.


FORMULA

a(n) = A355800(n)  A355799(n) + 1 by Euler's formula.


CROSSREFS

Cf. A355799 (vertices), A355800 (edges), A355801 (kgons), A255011 (all vertices), A290131, A331452, A335678.
Sequence in context: A260217 A048806 A043009 * A006736 A165752 A166036
Adjacent sequences: A355795 A355796 A355797 * A355799 A355800 A355801


KEYWORD

nonn


AUTHOR

Scott R. Shannon, Jul 17 2022


STATUS

approved



