%I #6 Jan 06 2024 23:58:33

%S 2,4,12,48,150,288,728,1344,1782,3780,5852,7224,12350,17108,16620,

%T 30720,40018,46728,64676,80560,84462,121044,146280,163728,208250,

%U 245700,271836,335664,389006,404400,514352,587264,638022,756228,853300,933480,1074998,1200724,1295112,1485120,1645002

%N 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.

%H Scott R. Shannon, <a href="/A368814/a368814.png">Image for n = 2</a>.

%H Scott R. Shannon, <a href="/A368814/a368814_1.png">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A368814/a368814_2.png">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A368814/a368814_3.png">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A368814/a368814_4.png">Image for n = 6</a>.

%H Scott R. Shannon, <a href="/A368814/a368814_5.png">Image for n = 10</a>.

%H Scott R. Shannon, <a href="/A368814/a368814_6.png">Image for n = 15</a>. 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.

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

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

%K nonn

%O 1,1

%A _Scott R. Shannon_, Jan 06 2024