A331222 a(n) = numerator of squared radius R^2 of the circumcircle of the n-th non-obtuse triangle with integer sides i <= j <= k <= sqrt(i^2 + j^2) in a list of such triangles, the list being sorted by increasing size of R. Denominators are A331223.

1, 16, 4, 81, 81, 3, 81, 256, 64, 256, 16, 25, 625, 625, 256, 625, 625, 25, 1296, 64, 324, 48, 625, 81, 1296, 12, 625, 3136, 2401, 2401, 1225, 2401, 2401, 1296, 2401, 2401, 50176, 4096, 81, 1024, 49, 49, 4096, 256, 256, 4096, 2401, 1024, 4096, 35721, 6561

Offset: 1

Author

Hugo Pfoertner, Jan 12 2020

Keywords

• nonn
• frac

Comments

Radii shared by more than one triangle are not removed. The first occurrence is for squared radius 49/3 at positions n = 41 and n = 42.

Examples

			The first terms b(n) = a(n)/A331223(n) correspond to the following triangles (i, j, k):
  b(1) = 1/3: (1,1,1),
  b(2) = 16/15: (1,2,2),
  b(3) = 4/3: (2,2,2),
  b(4) = 81/35: (1,3,3),
  b(5) = 81/32: (2,3,3),
  b(6) = 3/1: (3,3,3),
  b(7) = 81/20: (3,3,4),
  b(8) = 256/63: (1,4,4),
  b(9) = 64/15: (2,4,4),
...
  b(41) = b(42) = 49/3: (5,7,8), (7,7,7).
		

Crossrefs

Cf. A317182, A331223, A331227, A331228.

Formula

Squared radius of circumcircle of triangle with sides a, b, c:

R^2 = (a*b*c)^2 / (16*s*(s - a)*(s - b)*(s - c)) with s = (a + b + c)/2.