OFFSET
1,1
COMMENTS
See the linked references for further details.
The first diagram where not all edge points are connected is n = 3. For example a line connecting points (0,1/3) and (1/3,0) has equation 3*y - 6*x - 1 = 0, and as one of the x or y coefficients is greater than n (3 in this case) the line is not included.
It would be nice to have a proof (or disproof) that the number of sides is always 3 or 4.
LINKS
Alain Daurat et al., About the frequencies of some patterns in digital planes. Application to area estimators. Computers & graphics. 33.1 (2009), 11-20.
Daniel Khoshnoudirad, Farey lines defining Farey diagrams and application to some discrete structures. Applicable Analysis and Discrete Mathematics. 9 (2015), 73-84.
Scott R. Shannon, Image for n = 5.
Wikipedia, Farey sequence.
FORMULA
Sum of row n = A358882(n).
EXAMPLE
The table begins:
4;
48, 8;
400, 104;
1568, 456;
6216, 1848;
13944, 4256;
38760, 11976;
75768, 23480;
154440, 48248;
261072, 82184;
500464, 157440;
747480, 235528;
1298584, 410088;
1890184, 595784;
2853416, 901768;
4015552, 1274392;
6127632, 1942104;
8002552, 2537240;
11683880, 3703440;
15123800, 4790040;
.
.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Scott R. Shannon and N. J. A. Sloane, Dec 05 2022
STATUS
approved