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.

0, 40, 60, 12, 0, 484, 583, 160, 28, 8, 0, 2196, 2416, 804, 104, 28, 0, 5676, 6616, 2184, 460, 40, 8, 13456, 16936, 5236, 1340, 104, 12, 4, 27512, 35032, 11796, 2400, 320, 28, 0, 4, 0, 50688, 65044, 22536, 4632, 584, 60, 12, 4, 8, 84300, 105860, 38024, 8124, 1080, 108

Offset: 1

Author

Scott R. Shannon, Mar 18 2023

Keywords

• nonn
• tabf

Comments

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).

See A354605 and A353782 for images of the vertices and regions.

Examples

			The table begins:
 0, 40, 60, 12;
 0, 484, 583, 160, 28, 8;
 0, 2196, 2416, 804, 104, 28;
 0, 5676, 6616, 2184, 460, 40;
 8, 13456, 16936, 5236, 1340, 104, 12;
 4, 27512, 35032, 11796, 2400, 320, 28, 0, 4;
 0, 50688, 65044, 22536, 4632, 584, 60, 12, 4;
 8, 84300, 105860, 38024, 8124, 1080, 108;
.
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Crossrefs

Cf. A354605 (vertices), A353782 (regions), A356358 (edges), A361622 (distinct circles), A359935, A359862, A359258, A359619, A359061.

Formula

Sum of row n = A353782(n).