A359859 Number of vertices among all distinct circles that can be constructed from a 2 x n square grid of points using only a compass.

2, 40, 190, 740, 1824, 3956, 7314, 12956, 20684, 32276, 47348, 68516, 94550, 128780, 170106, 222252, 283418, 358756

Offset

1,1

Comments

A circle is constructed for every pair of the 2 x n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed from the 2 x n points is conjectured to be 4*A001859(n-1).

No formula for a(n) is known.

Links

Table of n, a(n) for n=1..18.

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.

Scott R. Shannon, Image for n = 5.

Scott R. Shannon, Image for n = 6.

Formula

a(n) = A359861(n) - A359860(n) + 1 by Euler's formula.

Crossrefs

Cf. A359860 (regions), A359861 (edges), A359862 (k-gons), A001859, A359252.

Sequence in context: A269544 A281761 A370069 * A012477 A003760 A228240

Adjacent sequences: A359856 A359857 A359858 * A359860 A359861 A359862

Keyword

nonn,more

Author

Scott R. Shannon, Jan 16 2023

Status

approved