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A359258 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 n equally spaced points along a line using only a compass.

%I A359258 #20 Feb 06 2023 09:59:08
%S A359258 3,0,8,4,2,0,22,23,4,2,0,50,52,12,2,0,110,103,36,6,0,190,200,64,12,0,
%T A359258 314,387,88,28,4,0,498,606,152,32,8,0,770,941,228,58,4,2,0,1132,1352,
%U A359258 338,68,12,2,0,1602,1935,532,98,4,0,2122,2798,684,106,16,0,2850,3843,940,132,24,6
%N A359258 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 n equally spaced points along a line using only a compass.
%C A359258 A circle is constructed for every pair of the n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed for n points is A001859(n-1).
%C A359258 See A359252 and A359253 for other images of the circles.
%H A359258 Scott R. Shannon, <a href="/A359258/a359258.jpg">Image for n = 12</a>.
%F A359258 Sum of row n = A359253(n);
%e A359258 The table begins:
%e A359258   3;
%e A359258   0,     8,     4,    2;
%e A359258   0,    22,    23,    4,   2;
%e A359258   0,    50,    52,   12,   2;
%e A359258   0,   110,   103,   36,   6;
%e A359258   0,   190,   200,   64,  12;
%e A359258   0,   314,   387,   88,  28,  4;
%e A359258   0,   498,   606,  152,  32,  8;
%e A359258   0,   770,   941,  228,  58,  4,  2;
%e A359258   0,  1132,  1352,  338,  68, 12,  2;
%e A359258   0,  1602,  1935,  532,  98,  4;
%e A359258   0,  2122,  2798,  684, 106, 16;
%e A359258   0,  2850,  3843,  940, 132, 24,  6;
%e A359258   0,  3774,  4998, 1268, 192, 28,  6;
%e A359258   0,  4950,  6475, 1644, 276, 44, 10;
%e A359258   0,  6190,  8454, 1978, 326, 74,  4;
%e A359258   0,  7778, 10737, 2520, 434, 52, 12, 4;
%e A359258   0,  9674, 13224, 3202, 528, 58, 12, 4;
%e A359258   0, 11978, 16169, 4116, 640, 68, 20, 4;
%e A359258   ...
%Y A359258 Cf. A359253 (regions), A359252 (vertices), A359254 (edges), A001859, A332723, A359061, A359009.
%K A359258 nonn,tabf
%O A359258 2,1
%A A359258 _Scott R. Shannon_, Dec 23 2022