A354605 Number of vertices 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.

101, 1145, 5001, 13753, 34497, 72185, 135157, 224321

Offset

1,1

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).

No formula for a(n) is currently known.

Links

Table of n, a(n) for n=1..8.

Scott R. Shannon, Image for n = 1.

Scott R. Shannon, Image for n = 2.

Scott R. Shannon, Image for n = 3.

Formula

a(n) = A356358 - A353782(n) + 1 by Euler's formula.

Crossrefs

Cf. A353782 (regions), A356358 (edges), A361623 (k-gons), A361622 (distinct circles), A359932, A359859, A359252, A359569, A331702.

Sequence in context: A290827 A290835 A290549 * A275986 A368416 A215119

Adjacent sequences: A354602 A354603 A354604 * A354606 A354607 A354608

Keyword

nonn,more

Author

Scott R. Shannon, Mar 13 2023

Status

approved