A367122 Place n points in general position on each side of a square, and join every pair of the 4*n+4 boundary points by a chord; sequence gives number of edges in the resulting planar graph.

8, 124, 780, 2816, 7480, 16428, 31724, 55840, 91656, 142460, 211948, 304224, 423800, 575596, 764940, 997568, 1279624, 1617660, 2018636, 2489920, 3039288, 3674924, 4405420, 5239776, 6187400, 7258108, 8462124, 9810080, 11313016, 12982380, 14830028, 16868224, 19109640, 21567356

Offset: 0

Author

Scott R. Shannon and N. J. A. Sloane, Nov 05 2023

Keywords

• nonn

Comments

"In general position" implies that the internal lines (or chords) only have simple intersections. There is no interior point where three or more chords meet.

See A334698 and A367121 for images of the square.

Crossrefs

Cf. A334698 (vertices), A367121 (regions), A331448, A367119.

Formula

Conjecture: a(n) = 17*n^4 + 38*n^3 + 37*n^2 + 24*n + 8.

a(n) = A334698(n+1) + A367121(n) - 1 by Euler's formula.