A360351 Number of vertices among all distinct circles that can be constructed from an n X n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle.

5, 77, 1045, 6885, 30265, 104421, 309973, 800185, 1862053

Offset

2,1

Comments

A circle is constructed for every pair of points on the n X n grid, the points lying at the ends of a diameter of the circle. The number of distinct circles constructed from the n X n grid is A360350(n).

Links

Table of n, a(n) for n=2..10.

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.

N. J. A. Sloane, New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Doron Zeilberger's Exper. Math. Seminar, Rutgers, Sep 14 2023: Video, Slides, Updates. (Mentions this sequence.)

Formula

a(n) = A360353(n) - A360352(n) + 1 by Euler's formula.

Crossrefs

Cf. A360352 (regions), A360353 (edges), A360354 (k-gons), A360350 (distinct circles), A359932.

Sequence in context: A186662 A186660 A287041 * A318236 A009485 A188455

Adjacent sequences: A360348 A360349 A360350 * A360352 A360353 A360354

Keyword

nonn,more

Author

Scott R. Shannon, Feb 03 2023

Status

approved