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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.
9
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
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
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Jul 18 2022
STATUS
approved