A362236 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 when each pair of points is connected by a circle and where the points lie at the ends of the circles' diameter.

12, 12, 8, 32, 204, 120, 16, 56, 928, 652, 156, 4, 8, 72, 2724, 2332, 504, 120, 16, 4, 96, 6416, 6120, 1648, 352, 20, 8, 128, 13356, 12444, 4156, 668, 52, 12, 208, 24348, 23892, 8148, 1488, 124, 24, 248, 41268, 41528, 14108, 2616, 276, 36, 336, 65684, 67272, 23372, 4592, 388, 52, 0, 4

Offset

1,1

Comments

A circle is constructed for every pair of the 1 + 4n points, the two points lying at the ends of a diameter of the circle. The number of distinct circles constructed from the points is A139275(n).

See A362233 and A362234 for images of the circles.

Links

Table of n, a(n) for n=1..57.

Formula

Sum of row n = A362234(n).

Example

The table begins:
 12, 12, 8;
 32, 204, 120, 16;
 56, 928, 652, 156, 4, 8;
 72, 2724, 2332, 504, 120, 16, 4;
 96, 6416, 6120, 1648, 352, 20, 8;
 128, 13356, 12444, 4156, 668, 52, 12;
 208, 24348, 23892, 8148, 1488, 124, 24;
 248, 41268, 41528, 14108, 2616, 276, 36;
 336, 65684, 67272, 23372, 4592, 388, 52, 0, 4;
 384, 99440, 105260, 36028, 7316, 708, 60, 4;
 464, 144684, 156976, 54136, 10792, 1224, 100, 8;
 .
 .

Crossrefs

Cf. A362233 (vertices), A362234 (regions), A362235 (edges), A139275 (distinct circles), A361623, A359935.

Sequence in context: A118877 A112124 A268916 * A069873 A129498 A010851

Adjacent sequences: A362233 A362234 A362235 * A362237 A362238 A362239

Keyword

nonn,tabf

Author

Scott R. Shannon, Apr 13 2023

Status

approved