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%I #13 Dec 06 2022 19:33:37
%S 8,92,816,3276,13040,29452,82128,160656,328212,556040,1065660,1592368,
%T 2768168,4026972,6083804,8572272,13075848,17078512,24932940,32266036
%N The number of edges in a Farey diagram of order (n,n).
%C See the linked references for further details.
%C 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.
%H Alain Daurat et al., <a href="https://doi.org/10.1016/j.cag.2008.11.001">About the frequencies of some patterns in digital planes. Application to area estimators</a>. Computers & graphics. 33.1 (2009), 11-20.
%H Daniel Khoshnoudirad, <a href="https://doi.org/10.2298/AADM150219008K">Farey lines defining Farey diagrams and application to some discrete structures</a>. Applicable Analysis and Discrete Mathematics. 9 (2015), 73-84.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Farey_sequence">Farey sequence</a>.
%F a(n) = A358882(n) + A358883(n) - 1 by Euler's formula.
%Y Cf. A358882 (regions), A358883 (vertices), A358885 (k-gons), A006842, A006843, A005728, A358888.
%Y See A358298 for definition of Farey diagram Farey(m,n).
%Y The Farey Diagrams Farey(m,n) are studied in A358298-A358307 and A358882-A358885, the Completed Farey Diagrams of order (m,n) in A358886-A358889.
%K nonn,more
%O 1,1
%A _Scott R. Shannon_ and _N. J. A. Sloane_, Dec 05 2022
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