A368814 - OEIS

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.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..41.

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

Adjacent sequences: A368811 A368812 A368813 * A368815 A368816 A368817

KEYWORD

nonn

AUTHOR

Scott R. Shannon, Jan 06 2024

STATUS

approved