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 A358882 The number of regions in a Farey diagram of order (n,n). 25
 4, 56, 504, 2024, 8064, 18200, 50736, 99248, 202688, 343256, 657904, 983008, 1708672, 2485968, 3755184, 5289944, 8069736, 10539792, 15387320, 19913840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A358298 and also 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. LINKS Table of n, a(n) for n=1..20. Alain Daurat, M. Tajine, M. Zouaoui, 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 = 1. Scott R. Shannon, Image for n = 2. Scott R. Shannon, Image for n = 3. Scott R. Shannon, Image for n = 4. Scott R. Shannon, Image for n = 5. Scott R. Shannon, Image for n = 6. Scott R. Shannon, Image for n = 7. Scott R. Shannon, Image for n = 8. Wikipedia, Farey sequence. FORMULA a(n) = A358884(n) - A358883(n) + 1 by Euler's formula. CROSSREFS Cf. A358883 (vertices), A358884 (edges), A358885 (k-gons), A006842, A006843, A005728, A358886. See A358298 for definition of Farey diagram Farey(m,n). 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. Sequence in context: A077122 A020540 A101540 * A224181 A026740 A191466 Adjacent sequences: A358879 A358880 A358881 * A358883 A358884 A358885 KEYWORD nonn,more AUTHOR Scott R. Shannon and N. J. A. Sloane, Dec 05 2022 STATUS approved

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Last modified July 12 19:36 EDT 2024. Contains 374252 sequences. (Running on oeis4.)