A359570 Number of regions after n iterations of constructing circles from all current vertices using only a compass, starting with one vertex. See the Comments.

0, 1, 3, 21, 7169

Offset

1,3

Comments

See A359569 for further details and images.

Links

Table of n, a(n) for n=1..5.

Scott R. Shannon, Image for 3-region figure (black background). In this and other images the vertices used to construct the circles are shown as white dots.

Scott R. Shannon, Image for 3-region figure (white background).

Scott R. Shannon, Image for 21-region figure (black background).

Scott R. Shannon, Image for 21-region figure (white background).

Scott R. Shannon, Image for 7169-region figure (black background).

Scott R. Shannon, Image for 7169-region figure (white background).

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

For n >= 3, a(n) = A359571(n) - A359569(n) + 1 by Euler's formula.

Crossrefs

Cf. A359569 (vertices), A359571 (edges), A359619 (k-gons), A359253, A359046, A358782.

Sequence in context: A117508 A331897 A001139 * A341086 A277628 A016449

Adjacent sequences: A359567 A359568 A359569 * A359571 A359572 A359573

Keyword

nonn,more,hard

Author

Scott R. Shannon, Jan 06 2023

Status

approved