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A360044
Table read by rows: T(n,k) is the number of k-gons, 3<=k<=4, in a Farey fan of order n.
3
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
1,3
COMMENTS
See the reference for the definition of a 'Farey fan', along with a proof that only 3-gons and 4-gons are created. See A360042 for further details and images of the graph.
LINKS
M. D. McIlroy, A Note on Discrete Representation of Lines, AT&T Technical Journal, 64 (1985), 481-490.
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 = 10.
EXAMPLE
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;
.
.
CROSSREFS
Cf. A005598 (regions), A360042 (vertices), A360043 (edges), A005728, A174030, A359977, A359971, A359694.
Sequence in context: A353005 A010637 A200692 * A127447 A226775 A338682
KEYWORD
nonn,tabf
STATUS
approved