A360354 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 an n x n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle.

8, 4, 40, 108, 20, 92, 904, 456, 76, 0, 8, 200, 4540, 3400, 652, 100, 4, 8, 404, 17244, 15324, 3148, 628, 116, 16, 528, 54252, 54476, 11672, 2152, 332, 44, 12, 972, 151992, 158468, 37244, 7940, 1120, 224, 48, 12, 16, 1404, 379488, 404148, 103436, 20216, 3316, 600, 132, 20, 16

Offset

2,1

Comments

A circle is constructed for every pair of points on the n X n grid, the points lying at the ends of a diameter of the circle.

The number of distinct circles constructed from the n x n grid is A360350(n).

See A360351 and A360352 for images of the circles.

Links

Table of n, a(n) for n=2..54.

Formula

Sum of row n = A360352(n).

Example

The table begins:
8, 4;
40, 108, 20;
92, 904, 456, 76, 0, 8;
200, 4540, 3400, 652, 100, 4, 8;
404, 17244, 15324, 3148, 628, 116, 16;
528, 54252, 54476, 11672, 2152, 332, 44, 12;
972, 151992, 158468, 37244, 7940, 1120, 224, 48, 12, 16;
1404, 379488, 404148, 103436, 20216, 3316, 600, 132, 20, 16;
1896, 868460, 923656, 252096, 49848, 7916, 1744, 276, 84;
.
.

Crossrefs

Cf. A360351 (vertices), A360352 (regions), A360353 (edges), A360354 (k-gons), A360350 (distinct circles), A359935.

Sequence in context: A270729 A270465 A270980 * A270317 A270329 A270626

Adjacent sequences: A360351 A360352 A360353 * A360355 A360356 A360357

Keyword

nonn,tabf

Author

Scott R. Shannon, Feb 04 2023

Status

approved