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

Offset: 1

Author

Scott R. Shannon, Jan 06 2024

Keywords

• nonn

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.

Crossrefs

Cf. A368813 (regions), A368815 (edges), A368816 (k-gons), A368756, A007569.

Formula

a(n) = A368815(n) - A368813(n) + 1 by Euler's formula.