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A368814
Number of vertices in a regular 2n-gon when all vertices are connect by straight lines except for the n lines joining diametrically opposite vertices.
4
2, 4, 12, 48, 150, 288, 728, 1344, 1782, 3780, 5852, 7224, 12350, 17108, 16620, 30720, 40018, 46728, 64676, 80560, 84462, 121044, 146280, 163728, 208250, 245700, 271836, 335664, 389006, 404400, 514352, 587264, 638022, 756228, 853300, 933480, 1074998, 1200724, 1295112, 1485120, 1645002
OFFSET
1,1
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 = 10.
Scott R. Shannon, Image for n = 15. Note that the maximum number of chord crossings on a single vertex is six for this 30-gon, which is one less than the maximum theoretical value of seven for the regular n-gon with all diagonals drawn; see A007569.
FORMULA
a(n) = A368815(n) - A368813(n) + 1 by Euler's formula.
CROSSREFS
Cf. A368813 (regions), A368815 (edges), A368816 (k-gons), A368756, A007569.
Sequence in context: A131387 A207647 A152453 * A277281 A172452 A004527
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Jan 06 2024
STATUS
approved