A359860 Number of regions among all distinct circles that can be constructed from a 2 X n square grid of points using only a compass.

3, 45, 231, 865, 2081, 4489, 8211, 14401, 22857, 35445, 51741, 74397, 102271, 138801, 182739, 238181, 303175, 383097, 474995, 586021, 712003, 860829, 1028225, 1223773, 1440593, 1689993, 1965525, 2279509, 2622993, 3011405, 3433615, 3907241, 4419261, 4988781, 5603271

Offset

1,1

Comments

See A359859 for further details. No formula for a(n) is known.

Links

Table of n, a(n) for n=1..35.

Lucas A. Brown, Python program.

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 = 8.

Formula

a(n) = A359861(n) - A359859(n) + 1 by Euler's formula.

Crossrefs

Cf. A359859 (vertices), A359861 (edges), A359862 (k-gons), A001859, A359253.

Sequence in context: A069955 A289193 A062346 * A002682 A073595 A370954

Adjacent sequences: A359857 A359858 A359859 * A359861 A359862 A359863

Keyword

nonn

Author

Scott R. Shannon, Jan 16 2023

Extensions

a(19)-a(35) from Lucas A. Brown, Oct 11 2024

Status

approved