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A372734 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 when every pair of the 3 + 3*n points are connected by a circle and where the points lie at the ends of the circle's diameter.

%I A372734 #6 May 12 2024 10:04:37
%S A372734 0,7,12,61,9,6,6,303,108,9,9,3,18,771,603,150,15,9,0,1,24,1722,1740,
%T A372734 339,81,3,0,1,30,3789,4326,1104,234,18,3,36,6907,8274,2193,432,45,18,
%U A372734 66,12012,15504,4173,922,105,45,3,3,90,19860,24774,7389,1773,150,30,48,30594,39852,12438,2998,387,48
%N A372734 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 when every pair of the 3 + 3*n points are connected by a circle and where the points lie at the ends of the circle's diameter.
%C A372734 A circle is constructed for every pair of the 3 + 3*n points, the two points lying at the ends of a diameter of the circle.
%C A372734 See A372731 and A372732 for images of the circles.
%F A372734 Sum of row(n) = A372732(n).
%e A372734 The table begins:
%e A372734 0, 7;
%e A372734 12, 61, 9, 6;
%e A372734 6, 303, 108, 9, 9, 3;
%e A372734 18, 771, 603, 150, 15, 9, 0, 1;
%e A372734 24, 1722, 1740, 339, 81, 3, 0, 1;
%e A372734 30, 3789, 4326, 1104, 234, 18, 3;
%e A372734 36, 6907, 8274, 2193, 432, 45, 18;
%e A372734 66, 12012, 15504, 4173, 922, 105, 45, 3, 3;
%e A372734 90, 19860, 24774, 7389, 1773, 150, 30;
%e A372734 48, 30594, 39852, 12438, 2998, 387, 48;
%e A372734 96, 45456, 59019, 18669, 4429, 609, 93, 3, 6;
%e A372734 90, 66633, 86088, 29136, 6840, 1164, 195, 6;
%e A372734 120, 90210, 121614, 40035, 9160, 1362, 177, 12, 9;
%e A372734 108, 124245, 167646, 57048, 14377, 1989, 300, 33, 15;
%e A372734 .
%e A372734 .
%Y A372734 Cf. A372731 (vertices), A372732 (regions), A372733 (edges), A372735 (number of circles), A372617, A371376, A361623, A360354.
%K A372734 nonn,tabf
%O A372734 0,2
%A A372734 _Scott R. Shannon_, May 12 2024