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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.
3
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
1,2
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.
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.
EXAMPLE
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
KEYWORD
nonn,frac
AUTHOR
Hugo Pfoertner, Jan 12 2020
STATUS
approved