cp's OEIS Frontend

A374828 Irregular table read by rows: Place n equally spaced points on the circumference of a circle of radius r and then connect each pair of points with straight lines whose intersections create A007569(n) - n additional points. Draw a circle of radius r around each of the A007569(n) points. T(n,k) is the number of k-sided regions, k>=2, formed from all circle intersections.

%I A374828 #19 Jul 24 2024 08:59:40
%S A374828 3,3,0,12,4,5,45,10,10,10,0,156,84,48,30,6,0,742,476,294,119,21,14,0,
%T A374828 1104,1296,512,152,40,16,0,6669,6768,2790,1179,207,81,9,0,10280,11130,
%U A374828 5490,1440,260,150,20,10,0,40777,45342,20669,6963,1177,374,77,11,11
%N A374828 Irregular table read by rows: Place n equally spaced points on the circumference of a circle of radius r and then connect each pair of points with straight lines whose intersections create A007569(n) - n additional points. Draw a circle of radius r around each of the A007569(n) points. T(n,k) is the number of k-sided regions, k>=2, formed from all circle intersections.
%C A374828 It is likely that n = 5 is the last graph that produces 2-sided regions, although this is unknown.
%H A374828 Scott R. Shannon, <a href="/A374828/a374828_1.jpg">Image for n = 5</a>. The starting circles' centers are shown as white dots.
%H A374828 Scott R. Shannon, <a href="/A374828/a374828.jpg">Image for n = 7</a>.
%F A374828 Sum of row n = A374826(n).
%e A374828 The table begins:
%e A374828 3, 3;
%e A374828 0, 12, 4;
%e A374828 5, 45, 10, 10, 10;
%e A374828 0, 156, 84, 48, 30, 6;
%e A374828 0, 742, 476, 294, 119, 21, 14;
%e A374828 0, 1104, 1296, 512, 152, 40, 16;
%e A374828 0, 6669, 6768, 2790, 1179, 207, 81, 9;
%e A374828 0, 10280, 11130, 5490, 1440, 260, 150, 20, 10;
%e A374828 0, 40777, 45342, 20669, 6963, 1177, 374, 77, 11, 11;
%e A374828 0, 33672, 39552, 16236, 5772, 1080, 288, 0, 12, 0, 12;
%e A374828 0, 181467, 212186, 97461, 30082, 5252, 1430, 78, 104, 0, 0, 13;
%e A374828 0, 198772, 246134, 104356, 33348, 5614, 1190, 252, 28, 0, 0, 0, 14;
%e A374828 .
%e A374828 .
%Y A374828 Cf. A374825 (vertices), A374826 (regions), A374827 (edges), A007569 (total circles).
%K A374828 nonn,tabf
%O A374828 3,1
%A A374828 _Scott R. Shannon_, Jul 21 2024