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

0,1

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.

Links

Table of n, a(n) for n=0..33.

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.

Crossrefs

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

Sequence in context: A376099 A120957 A302356 * A069459 A254125 A371298

Adjacent sequences: A367119 A367120 A367121 * A367123 A367124 A367125

Keyword

nonn

Author

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

Status

approved