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Search: id:A146212
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| A146212 |
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Number of intersection points of all lines through the vertices of a regular n-gon. |
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+0
2
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| 3, 5, 15, 37, 91, 145, 333, 471, 891, 901, 1963, 2185, 3795, 3969, 6681, 5563, 10963, 11141, 17031, 17293, 25323, 21913, 36325, 36479, 50571, 50485, 68643, 51661, 91171, 90753, 118833, 118355, 152355, 139861, 192511, 191445, 240123, 238481
(list; graph; listen)
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OFFSET
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3,1
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COMMENT
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This includes intersection points outside of the n-gon. Note that for odd n, n divides a(n); for even n, n divides a(n)-1. For odd n, it appears that a(n)=n(n^3-7n^2+15n-1)/8.
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LINKS
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Jon Schoenfield, Table of n, a(n) for n = 3..100
T. D. Noe, Pentagon Illustrated [From T. D. Noe (noe(AT)sspectra.com), Oct 30 2008]
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EXAMPLE
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a(5)=15 because there are 5 points inside the pentagon, 5 points on the pentagon and five points outside of the pentagon.
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CROSSREFS
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A006561, A007569, A146213
Sequence in context: A148501 A148502 A089485 this_sequence A018516 A138017 A148503
Adjacent sequences: A146209 A146210 A146211 this_sequence A146213 A146214 A146215
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KEYWORD
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nice,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Oct 28 2008
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EXTENSIONS
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More terms from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Nov 10 2008
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