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Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square, using only a compass.

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`%I #7 May 19 2024 08:53:36
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`%S 16,29,272,260,80,12,4,1708,2253,528,120,20,4,5200,7636,2136,432,44,
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`%T 20,8,13732,20788,5712,1120,184,17,8,31576,49284,14060,3180,584,108,
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`%U 16,64748,103557,30372,6472,980,172,4,12,103368,166804,49920,11196,1660,260,48,16,181376,296388,88916,19844,3128,445,64,20
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`%N Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square, using only a compass.
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`%C A circle is constructed for every pair of the 4 + 4*n points, the first point defines the circle's center while the second the radius distance.
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`%C Unlike A372617, a similar sequence but with vertices on an equilateral triangle, for the terms studied no graph has 2-edged regions.
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`%C See A372977 and A372978 for images of the circles.
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`%F Sum of row n = A372978(n).
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`%e The table begins:
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`%e 16, 29;
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`%e 272, 260, 80, 12, 4;
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`%e 1708, 2253, 528, 120, 20, 4;
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`%e 5200, 7636, 2136, 432, 44, 20, 8;
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`%e 13732, 20788, 5712, 1120, 184, 17, 8;
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`%e 31576, 49284, 14060, 3180, 584, 108, 16;
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`%e 64748, 103557, 30372, 6472, 980, 172, 4, 12;
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`%e 103368, 166804, 49920, 11196, 1660, 260, 48, 16;
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`%e 181376, 296388, 88916, 19844, 3128, 445, 64, 20;
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`%e .
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`%e .
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`%Y Cf. A372977 (vertices), A372978 (regions), A372979 (edges), A372981 (circles), A372617, A371376, A361623, A360354.
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`%K nonn
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`%O 0,1
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`%A _Scott R. Shannon_, May 19 2024
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