A353782 Number of regions 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.

112, 1264, 5548, 14976, 37092, 77096, 143560, 237504

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.

Scott R. Shannon, Image for n = 4.

Formula

a(n) = A356358 - A354605(n) + 1 by Euler's formula.

Crossrefs

Cf. A354605 (vertices), A356358 (edges), A361623 (k-gons), A361622 (distinct circles), A359933, A359860, A359253, A359570, A359046.

Sequence in context: A232850 A233115 A188152 * A367363 A327633 A210300

Adjacent sequences: A353779 A353780 A353781 * A353783 A353784 A353785

Keyword

nonn,more

Author

Scott R. Shannon, Mar 13 2023

Status

approved