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A359971
Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions equal the Farey series of order n.
5
1, 5, 33, 15, 108, 126, 5, 727, 1031, 38, 2, 1314, 2452, 167, 15, 2, 6811, 12102, 988, 52, 14904, 27626, 3255, 214, 4, 2, 2, 39172, 73289, 10062, 795, 19, 1, 65833, 127951, 18476, 1464, 64, 5, 201643, 370880, 59630, 5548, 250, 7, 2, 288196, 541258, 91037, 9692, 428, 20, 4, 741597, 1351301, 239180, 27510, 1434, 58
OFFSET
1,2
COMMENTS
The number of vertices along the shorter edges is A005728(n).
No formula for a(n) is known. The sequence is inspired by the Farey fan; see A360042.
See A359968 and A359969 for images of the triangle.
EXAMPLE
The table begins:
1;
5;
33, 15;
108, 126, 5;
727, 1031, 38, 2;
1314, 2452, 167, 15, 2;
6811, 12102, 988, 52;
14904, 27626, 3255, 214, 4, 2, 2;
39172, 73289, 10062, 795, 19, 1;
65833, 127951, 18476, 1464, 64, 5;
201643, 370880, 59630, 5548, 250, 7, 2;
288196, 541258, 91037, 9692, 428, 20, 4;
741597, 1351301, 239180, 27510, 1434, 58;
1095197, 2025237, 374907, 44880, 2491, 104, 4, 2;
1747260, 3279178, 628335, 76787, 4600, 178, 6;
...
CROSSREFS
Cf. A359968 (vertices), A359969 (regions and row sums), A359970 (edges), A005728, A360042, A359977, A359694, A358951, A358889.
Sequence in context: A349099 A174471 A275233 * A043068 A194405 A299518
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved