login
A373110
Number of distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square when every pair of the 4 + 4*n points are connected by a circle and where the points lie at the ends of the circle's diameter.
4
5, 22, 54, 99, 159, 232, 320, 421, 537, 666, 810, 967, 1139, 1324, 1524, 1737, 1965, 2206, 2462, 2731, 3015, 3312, 3624, 3949
OFFSET
0,1
COMMENTS
A circle is constructed for every pair of the 4 + 4*n points, the two points lying at the ends of a diameter of the circle.
See A373106 and A373107 for images of the circles.
FORMULA
Conjectured:
For even n, a(n) = (14*n^2 + 21*n + 10)/2.
For odd n, a(n) = (14*n^2 + 21*n + 9)/2.
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon, May 25 2024
STATUS
approved