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%I #19 Jan 17 2021 11:29:53
%S 1,18,6,79,51,12,3,252,192,60,6,6,576,600,168,73,15,1170,1380,390,126,
%T 6,12,2248,2589,894,288,66,18,3,4026,4332,1662,480,108,30,6426,7182,
%U 2988,943,189,36,9942,11268,4470,1266,300,84,0,6,14508,16941,7098,2119,435,120,6,6
%N Irregular table read by rows: Take a Reuleaux triangle with all diagonals drawn, as in A340639. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.
%C See A340639 for images of the regions and A340644 for images of the vertices.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Reuleaux_triangle">Reuleaux triangle</a>.
%e A Reuleaux triangle with 1 point dividing its edges, n = 2, contains 18 triangles, 6 quadrilaterals and no other n-gons, so the second row is [18, 6]. A Reuleaux triangle with 2 points dividing its edges, n = 3, contains 79 triangles, 51 quadrilaterals, 12 pentagons, 3 hexagons and no other n-gons, so the third row is [79, 51, 12, 3].
%e The table begins:
%e 1;
%e 18, 6;
%e 79, 51, 12, 3;
%e 252, 192, 60, 6, 6;
%e 576, 600, 168, 73, 15;
%e 1170, 1380, 390, 126, 6, 12;
%e 2248, 2589, 894, 288, 66, 18, 3;
%e 4026, 4332, 1662, 480, 108, 30;
%e 6426, 7182, 2988, 943, 189, 36;
%e 9942, 11268, 4470, 1266, 300, 84, 0, 6;
%e 14508, 16941, 7098, 2119, 435, 120, 6, 6;
%e 21234, 23598, 10194, 3090, 636, 132, 12, 6;
%e 28881, 34086, 13935, 4528, 1041, 177, 24, 3;
%e 39588, 45384, 19470, 5796, 1380, 198, 48;
%e 52197, 60744, 26409, 7831, 1914, 366, 21, 15;
%e 68646, 78492, 33810, 10668, 2358, 396, 60;
%e 87642, 100701, 44670, 13942, 2931, 555, 66, 21, 6;
%e 111084, 127290, 55818, 17082, 3912, 696, 132, 6;
%e 138453, 158907, 70158, 22233, 4869, 1002, 87, 15, 0, 4;
%e 171276, 194622, 87312, 26748, 6132, 846, 174, 6, 6;
%Y Cf. A340639 (regions), A340644 (vertices), A340613 (edges), A007678, A092867.
%K nonn,tabf
%O 1,2
%A _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 14 2021
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