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A358889
Table read by rows: T(n,k) = number of k-gons, k >= 3, formed inside a square with edge length 1 by the straight line segments mutually connecting all vertices and points that divide the sides into segments with lengths equal to the Farey series of order n = A006842(n,m)/A006843(n,m), m = 1..A005728(n).
23
4, 48, 8, 712, 304, 24, 3368, 2400, 280, 16, 27424, 20360, 4784, 504, 32, 56000, 47088, 10912, 1400, 88, 8, 292424, 255608, 69368, 11504, 960, 56, 658800, 590208, 175856, 30160, 2496, 200, 24, 1748112, 1593912, 506496, 93584, 9616, 520, 24, 2981448, 2778456, 890368, 166912, 17192, 1144, 48
OFFSET
1,1
COMMENTS
The number of points along each edge is given by A005728(n).
LINKS
FORMULA
Sum of row n = A358886(n).
EXAMPLE
The table begins:
4;
48, 8;
712, 304, 24;
3368, 2400, 280, 16;
27424, 20360, 4784, 504, 32;
56000, 47088, 10912, 1400, 88, 8;
292424, 255608, 69368, 11504, 960, 56;
658800, 590208, 175856, 30160, 2496, 200, 24;
1748112, 1593912, 506496, 93584, 9616, 520, 24;
2981448, 2778456, 890368, 166912, 17192, 1144, 48;
.
.
CROSSREFS
Cf. A358886 (regions), A358887 (vertices), A358888 (edges), A006842, A006843, A005728, A358885.
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: A010293 A334699 A358885 * A225987 A377055 A178429
KEYWORD
nonn,more,tabl
AUTHOR
STATUS
approved