A362233 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 when each pair of points is connected by a circle and where the points lie at the ends of the circles' diameter.

17, 249, 1381, 4745, 12581, 26861, 51649, 89357, 145501, 225621, 335497

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).

No formula for a(n) is currently known.

Links

Table of n, a(n) for n=1..11.

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) = A362235(n) - A362234(n) + 1 by Euler's formula.

Crossrefs

Cf. A362234 (regions), A362235 (edges), A362236 (k-gons), A139275 (distinct circles), A354605, A359932.

Sequence in context: A324358 A294608 A294810 * A214175 A309856 A201302

Adjacent sequences: A362230 A362231 A362232 * A362234 A362235 A362236

Keyword

nonn,more

Author

Scott R. Shannon, Apr 12 2023

Status

approved