OFFSET
3,1
COMMENTS
Conjecture: the only n-gons that contain non-simple intersections are the 3-gon (triangle), 4-gon (square), and 6-gon (hexagon).
LINKS
Scott R. Shannon, Extended table for n = 3..50, k = 0..75.
FORMULA
EXAMPLE
The table begins:
3, 9, 27, 57, 99, 135, 219, 297, 351, 489, 603, 645, 867, 1017, ...
4, 12, 36, 76, 132, 180, 292, 348, 516, 604, 804, 892, 1156, 1284, ...
5, 15, 45, 95, 165, 255, 365, 495, 645, 815, 1005, 1215, 1445, 1695, ...
6, 18, 54, 114, 198, 306, 438, 594, 774, 942, 1206, 1422, 1734, 2034, ...
7, 21, 63, 133, 231, 357, 511, 693, 903, 1141, 1407, 1701, 2023, 2373, ...
8, 24, 72, 152, 264, 408, 584, 792, 1032, 1304, 1608, 1944, 2312, 2712, ...
9, 27, 81, 171, 297, 459, 657, 891, 1161, 1467, 1809, 2187, 2601, 3051, ...
10, 30, 90, 190, 330, 510, 730, 990, 1290, 1630, 2010, 2430, 2890, 3390, ...
11, 33, 99, 209, 363, 561, 803, 1089, 1419, 1793, 2211, 2673, 3179, 3729, ...
12, 36, 108, 228, 396, 612, 876, 1188, 1548, 1956, 2412, 2916, 3468, 4068, ...
13, 39, 117, 247, 429, 663, 949, 1287, 1677, 2119, 2613, 3159, 3757, 4407, ...
14, 42, 126, 266, 462, 714, 1022, 1386, 1806, 2282, 2814, 3402, 4046, 4746, ...
15, 45, 135, 285, 495, 765, 1095, 1485, 1935, 2445, 3015, 3645, 4335, 5085, ...
...
See the attached text file for further examples.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Scott R. Shannon, Sep 20 2022
STATUS
approved