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A361623 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 a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes using only a compass.

%I A361623 #10 Mar 22 2023 12:50:26
%S A361623 0,40,60,12,0,484,583,160,28,8,0,2196,2416,804,104,28,0,5676,6616,
%T A361623 2184,460,40,8,13456,16936,5236,1340,104,12,4,27512,35032,11796,2400,
%U A361623 320,28,0,4,0,50688,65044,22536,4632,584,60,12,4,8,84300,105860,38024,8124,1080,108
%N A361623 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 a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes using only a compass.
%C A361623 A circle is constructed for every pair of the 1 + 4n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed from the points is A361622(n).
%C A361623 See A354605 and A353782 for images of the vertices and regions.
%F A361623 Sum of row n = A353782(n).
%e A361623 The table begins:
%e A361623  0, 40, 60, 12;
%e A361623  0, 484, 583, 160, 28, 8;
%e A361623  0, 2196, 2416, 804, 104, 28;
%e A361623  0, 5676, 6616, 2184, 460, 40;
%e A361623  8, 13456, 16936, 5236, 1340, 104, 12;
%e A361623  4, 27512, 35032, 11796, 2400, 320, 28, 0, 4;
%e A361623  0, 50688, 65044, 22536, 4632, 584, 60, 12, 4;
%e A361623  8, 84300, 105860, 38024, 8124, 1080, 108;
%e A361623 .
%e A361623 .
%Y A361623 Cf. A354605 (vertices), A353782 (regions), A356358 (edges), A361622 (distinct circles), A359935, A359862, A359258, A359619, A359061.
%K A361623 nonn,tabf
%O A361623 1,2
%A A361623 _Scott R. Shannon_, Mar 18 2023