A359974
Number of vertices 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.
Original entry on oeis.org
3, 6, 26, 93, 424, 876, 2785, 5542, 11575, 18761, 40249, 57399, 109376, 155965, 227884, 322377, 532454, 676282, 1056010, 1334975, 1767798, 2240664, 3252047, 3882192, 5226897
Offset: 1
- McIlroy, M. D. "A Note on Discrete Representation of Lines". AT&T Technical Journal, 64 (1985), 481-490.
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.
Original entry on oeis.org
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
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;
...
A359975
Number of regions 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.
Original entry on oeis.org
1, 5, 30, 110, 479, 993, 3102, 6135, 12748, 20680, 43907, 62753, 118746, 168892, 246513, 348176, 571980, 725956, 1129035, 1426393, 1887096, 2387945, 3454566, 4123548, 5543837
Offset: 1
- McIlroy, M. D. "A Note on Discrete Representation of Lines". AT&T Technical Journal, 64 (1985), 481-490.
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.
Original entry on oeis.org
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
Offset: 1
- McIlroy, M. D. "A Note on Discrete Representation of Lines". AT&T Technical Journal, 64 (1985), 481-490.
A360044
Table read by rows: T(n,k) is the number of k-gons, 3<=k<=4, in a Farey fan of order n.
Original entry on oeis.org
0, 1, 4, 0, 6, 2, 10, 4, 14, 10, 22, 14, 30, 24, 42, 34, 54, 50, 74, 62, 94, 84, 118, 106, 142, 140, 178, 168, 214, 204, 258, 240, 302, 292, 358, 338, 414, 402, 478, 466, 542, 542, 626, 608, 710, 696, 802, 784, 894, 892, 1010, 988, 1126, 1102, 1254, 1216, 1382, 1358, 1526, 1492
Offset: 1
The table begins:
0, 1;
4, 0;
6, 2;
10, 4;
14, 10;
22, 14;
30, 24;
42, 34;
54, 50;
74, 62;
94, 84;
118, 106;
142, 140;
178, 168;
214, 204;
.
.
Showing 1-5 of 5 results.
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