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A372617 Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.

%I A372617 #12 May 10 2024 08:49:35
%S A372617 0,7,3,70,45,3,6,312,273,33,6,1017,1119,186,36,3,0,1,6,2943,4092,702,
%T A372617 150,15,3,1,6,6210,8556,1941,351,45,3,3,6,12946,20034,4632,735,99,9,6,
%U A372617 20925,32685,7944,1435,162,27,18,37704,59520,15375,2589,324,84,30,55326,87138,22626,4456,474,96,3
%N A372617 Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.
%C A372617 A circle is constructed for every pair of the 3 + 3*n points, the first point defines the circle's center while the second the radius distance.
%C A372617 See A372614 and A372615 for images of the circles.
%F A372617 Sum of row n = A372615(n).
%e A372617 The table begins:
%e A372617 0, 7;
%e A372617 3, 70, 45, 3;
%e A372617 6, 312, 273, 33;
%e A372617 6, 1017, 1119, 186, 36, 3, 0, 1;
%e A372617 6, 2943, 4092, 702, 150, 15, 3, 1;
%e A372617 6, 6210, 8556, 1941, 351, 45, 3, 3;
%e A372617 6, 12946, 20034, 4632, 735, 99, 9;
%e A372617 6, 20925, 32685, 7944, 1435, 162, 27;
%e A372617 18, 37704, 59520, 15375, 2589, 324, 84;
%e A372617 30, 55326, 87138, 22626, 4456, 474, 96, 3;
%e A372617 30, 91923, 146121, 38817, 7777, 894, 135, 9, 9;
%e A372617 36, 118734, 189804, 51747, 10356, 1122, 183;
%e A372617 36, 185730, 299571, 84285, 16015, 2139, 261, 3, 3;
%e A372617 .
%e A372617 .
%Y A372617 Cf. A372614 (vertices), A372615 (regions), A372616 (edges), A372682 (number of circles), A371376, A361623, A360354.
%K A372617 nonn,tabf
%O A372617 0,2
%A A372617 _Scott R. Shannon_, May 07 2024