cp's OEIS Frontend

A360044 Table read by rows: T(n,k) is the number of k-gons, 3<=k<=4, in a Farey fan of order n.

%I A360044 #16 Feb 02 2023 12:47:06
%S A360044 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 A360044 142,140,178,168,214,204,258,240,302,292,358,338,414,402,478,466,542,
%U A360044 542,626,608,710,696,802,784,894,892,1010,988,1126,1102,1254,1216,1382,1358,1526,1492
%N A360044 Table read by rows: T(n,k) is the number of k-gons, 3<=k<=4, in a Farey fan of order n.
%C A360044 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 A360044 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 A360044 Scott R. Shannon, <a href="/A360044/a360044.jpg">Image for n = 3</a>.
%H A360044 Scott R. Shannon, <a href="/A360044/a360044_1.jpg">Image for n = 4</a>.
%H A360044 Scott R. Shannon, <a href="/A360044/a360044_2.jpg">Image for n = 5</a>.
%H A360044 Scott R. Shannon, <a href="/A360044/a360044_3.jpg">Image for n = 6</a>.
%H A360044 Scott R. Shannon, <a href="/A360044/a360044_4.jpg">Image for n = 10</a>.
%e A360044 The table begins:
%e A360044 0, 1;
%e A360044 4, 0;
%e A360044 6, 2;
%e A360044 10, 4;
%e A360044 14, 10;
%e A360044 22, 14;
%e A360044 30, 24;
%e A360044 42, 34;
%e A360044 54, 50;
%e A360044 74, 62;
%e A360044 94, 84;
%e A360044 118, 106;
%e A360044 142, 140;
%e A360044 178, 168;
%e A360044 214, 204;
%e A360044 .
%e A360044 .
%Y A360044 Cf. A005598 (regions), A360042 (vertices), A360043 (edges), A005728, A174030, A359977, A359971, A359694.
%K A360044 nonn,tabf
%O A360044 1,3
%A A360044 _Scott R. Shannon_, _N. J. A. Sloane_ and _M. Douglas McIlroy_ , Jan 23 2023