login
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.
4
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved