%I #9 Jan 06 2024 23:58:19

%S 0,1,13,57,171,361,813,1489,2215,4081,6249,8329,13027,17977,20221,

%T 32033,41583,50545,66881,83161,93871,124521,150237,173233,213351,

%U 251473,285445,342889,397011,432121,524149,598081,663103,769217,867441,960121,1091723,1218889,1333489,1506321,1667799

%N Number of regions 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="/A368813/a368813.png">Image for n = 2</a>.

%H Scott R. Shannon, <a href="/A368813/a368813_1.png">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A368813/a368813_2.png">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A368813/a368813_3.png">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A368813/a368813_4.png">Image for n = 6</a>.

%H Scott R. Shannon, <a href="/A368813/a368813_5.png">Image for n = 10</a>.

%H Scott R. Shannon, <a href="/A368813/a368813_6.png">Image for n = 15</a>.

%F a(n) = A368815(n) - A368814(n) + 1 by Euler's formula.

%Y Cf. A368814 (vertices), A368815 (edges), A368816 (k-gons), A368755, A007678.

%K nonn

%O 1,3

%A _Scott R. Shannon_, Jan 06 2024