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A359976 Number of edges formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions on one edge equal the Farey series of order n while on the other they divide its length into n equal segments. 5
3, 10, 55, 202, 902, 1868, 5886, 11676, 24322, 39440, 84155, 120151, 228121, 324856, 474396, 670552, 1104433, 1402237, 2185044, 2761367, 3654893, 4628608, 6706612, 8005739, 10770733 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The number of vertices on the edge with point positions equaling the Farey series of order n is A005728(n). No formula for a(n) is known.
See A359974 and A359975 for images of the triangle.
This graph is related to the 'Farey fan' given in the reference.
REFERENCES
McIlroy, M. D. "A Note on Discrete Representation of Lines". AT&T Technical Journal, 64 (1985), 481-490.
LINKS
FORMULA
a(n) = A359974(n) + A359975(n) - 1 by Euler's formula.
CROSSREFS
Cf. A359974 (vertices), A359975 (regions), A359977 (k-gons), A005728, A359970, A359693, A358950, A358888.
Sequence in context: A229311 A208480 A342966 * A034234 A284645 A081721
KEYWORD
nonn,more
AUTHOR
STATUS
approved

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Last modified June 13 08:31 EDT 2024. Contains 373383 sequences. (Running on oeis4.)