A192493 Numerators of squared radii of circumcircles of non-degenerate triangles with integer vertex coordinates.

1, 1, 5, 25, 25, 2, 5, 25, 25, 13, 325, 169, 65, 4, 65, 17, 425, 221, 9, 289, 1105, 169, 85, 5, 325, 85, 50, 1105, 289, 25, 2125, 625, 13, 325, 425, 1625, 169, 1105, 125, 65, 29, 2465, 4225, 1885, 725, 377, 2465, 5525, 1885, 125, 8, 145, 65, 841, 17, 841, 845, 425, 2125, 221, 6409, 9425, 9, 325, 289, 145, 1105, 37, 5365, 3145, 169, 2405, 925, 85, 1369, 4625, 481, 625, 493, 2405, 10

Offset

1,3

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..9089, covering range R^2 <= 100.

Hugo Pfoertner, Circles Passing through 3 Points of the Square Lattice, illustrations up to R^2=10.

Example

The smallest triangle of lattice points {(0,0),(1,0),(0,1)} has circumradius R=sqrt(2)/2, i.e., R^2=1/2. Therefore a(1)=1, A192494(1)=2.

Crossrefs

Cf. A192494 (corresponding denominators), A128006, A128007.

Cf. A346993, A346994, A346995.

Sequence in context: A036139 A070382 A271379 * A265973 A265928 A039936

Adjacent sequences: A192490 A192491 A192492 * A192494 A192495 A192496

Keyword

nonn,frac

Author

Hugo Pfoertner, Jul 10 2011

Status

approved