A359253 Number of regions among all distinct circles that can be constructed from n equally spaced points along a line using only a compass.

3, 14, 51, 116, 255, 466, 821, 1296, 2003, 2904, 4171, 5726, 7795, 10266, 13399, 17026, 21537, 26702, 32995, 40110, 48511, 57996, 69121, 81376, 95511, 111130, 128953, 148432, 170595

Offset

2,1

Comments

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

No formula for a(n) is currently known.

Links

Table of n, a(n) for n=2..30.

Scott R. Shannon, Image for n = 2. In this and other images the n points are shown as white dots.

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.

Scott R. Shannon, Image for n = 10.

Scott R. Shannon, Image for n = 11.

Scott R. Shannon, Image for n = 20.

Formula

a(n) = A359254(n) - A359252(n) + 1 by Euler's formula.

Crossrefs

Cf. A359252 (vertices), A359254 (edges), A359258 (k-gons), A001859, A290865, A359046, A358782.

Sequence in context: A098521 A084150 A203196 * A320826 A322199 A192882

Adjacent sequences: A359250 A359251 A359252 * A359254 A359255 A359256

Keyword

nonn,more

Author

Scott R. Shannon, Dec 22 2022

Status

approved