

A359935


Irregular table read by rows: T(n,k) is the number of kgons, k>=2, among all distinct circles that can be constructed from an n x n square grid of points using only a compass.


8



0, 16, 30, 0, 412, 341, 60, 20, 4, 0, 3464, 3534, 928, 212, 48, 12, 0, 16936, 19861, 5252, 1056, 88, 52, 8, 0, 63712, 77394, 20480, 4820, 612, 108, 20, 12, 4, 202904, 244013, 71244, 14968, 1852, 472, 80, 32, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,2


COMMENTS

A circle is constructed for every pair of the n x n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed from the n x n points is A359931(n).
The first occurrence of a 2gon is when n = 7. Assuming the grid points are separated by 1 unit, in the first quadrant this region has endpoints (6,7) and (7,6)  an equivalent region is in each of the three other quadrants. Its arcs are from two circles, one with center at (2,2) going through point (2,3) while the other has center (3,3) going through point (0,1). See the attached image.


LINKS



FORMULA



EXAMPLE

The table begins:
0, 16, 30;
0, 412, 341, 60, 20, 4;
0, 3464, 3534, 928, 212, 48, 12;
0, 16936, 19861, 5252, 1056, 88, 52, 8;
0, 63712, 77394, 20480, 4820, 612, 108, 20, 12;
4, 202904, 244013, 71244, 14968, 1852, 472, 80, 32, 4;
.
.


CROSSREFS



KEYWORD

nonn,tabf,more


AUTHOR



STATUS

approved



