login
Number of edges among all distinct circles that can be constructed from a 2 X n square grid of points using only a compass.
5

%I #13 Oct 11 2024 07:56:17

%S 4,84,420,1604,3904,8444,15524,27356,43540,67720,99088,142912,196820,

%T 267580,352844,460432,586592,741852,920528,1136888,1382360,1672384,

%U 1998964,2380940,2804292,3291376,3830048,4444176,5116128,5876580,6703220,7631352,8634796,9751064,10956320

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

%C See A359859 and A359860 for further details and images of the circles. No formula for a(n) is known.

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A359859%2B60%2B61.py">Python program</a>.

%e a(n) = A359859(n) + A359860(n) - 1 by Euler's formula.

%Y Cf. A359859 (vertices), A359860 (regions), A359862 (k-gons), A001859, A359254.

%K nonn

%O 1,1

%A _Scott R. Shannon_, Jan 16 2023

%E a(19)-a(35) from _Lucas A. Brown_, Oct 11 2024