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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.
8
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
1,2
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.
FORMULA
Sum of row n = A353782(n).
EXAMPLE
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;
.
.
CROSSREFS
Cf. A354605 (vertices), A353782 (regions), A356358 (edges), A361622 (distinct circles), A359935, A359862, A359258, A359619, A359061.
Sequence in context: A260602 A116309 A126816 * A259061 A344408 A035120
KEYWORD
nonn,tabf
AUTHOR
Scott R. Shannon, Mar 18 2023
STATUS
approved