A368813 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.

0, 1, 13, 57, 171, 361, 813, 1489, 2215, 4081, 6249, 8329, 13027, 17977, 20221, 32033, 41583, 50545, 66881, 83161, 93871, 124521, 150237, 173233, 213351, 251473, 285445, 342889, 397011, 432121, 524149, 598081, 663103, 769217, 867441, 960121, 1091723, 1218889, 1333489, 1506321, 1667799

Offset

1,3

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.

Formula

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

Crossrefs

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

Sequence in context: A264853 A210290 A007202 * A222161 A218593 A358303

Adjacent sequences: A368810 A368811 A368812 * A368814 A368815 A368816

Keyword

nonn

Author

Scott R. Shannon, Jan 06 2024

Status

approved