A360044 - OEIS

%I #16 Feb 02 2023 12:47:06

%S 0,1,4,0,6,2,10,4,14,10,22,14,30,24,42,34,54,50,74,62,94,84,118,106,

%T 142,140,178,168,214,204,258,240,302,292,358,338,414,402,478,466,542,

%U 542,626,608,710,696,802,784,894,892,1010,988,1126,1102,1254,1216,1382,1358,1526,1492

%N Table read by rows: T(n,k) is the number of k-gons, 3<=k<=4, in a Farey fan of order n.

%C 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.

%H M. D. McIlroy, <a href="https://doi.org/10.1002/j.1538-7305.1985.tb00359.x">A Note on Discrete Representation of Lines</a>, AT&T Technical Journal, 64 (1985), 481-490.

%H Scott R. Shannon, <a href="/A360044/a360044.jpg">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A360044/a360044_1.jpg">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A360044/a360044_2.jpg">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A360044/a360044_3.jpg">Image for n = 6</a>.

%H Scott R. Shannon, <a href="/A360044/a360044_4.jpg">Image for n = 10</a>.

%e The table begins:

%e 0, 1;

%e 4, 0;

%e 6, 2;

%e 10, 4;

%e 14, 10;

%e 22, 14;

%e 30, 24;

%e 42, 34;

%e 54, 50;

%e 74, 62;

%e 94, 84;

%e 118, 106;

%e 142, 140;

%e 178, 168;

%e 214, 204;

%e .

%e .

%Y Cf. A005598 (regions), A360042 (vertices), A360043 (edges), A005728, A174030, A359977, A359971, A359694.

%K nonn,tabf

%O 1,3

%A _Scott R. Shannon_, _N. J. A. Sloane_ and _M. Douglas McIlroy_ , Jan 23 2023