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A331227 a(n) = numerator of squared radius R^2 of the circumcircle of the n-th triangle with integer sides i <= j <= k in a list of such triangles, the list being sorted by increasing size of R. Denominators are A331228.

%I A331227 #8 Jan 13 2020 15:20:19
%S A331227 1,16,4,16,81,81,3,81,256,64,64,256,16,25,625,625,256,625,1600,81,625,
%T A331227 25,2025,1296,64,64,324,48,625,81,400,1296,5184,12,625,3136,2401,3969,
%U A331227 2401,1225,1225,2401,2401,1296,2401,784,2401,50176,6400,4096,81,1024,49,49,49,49
%N A331227 a(n) = numerator of squared radius R^2 of the circumcircle of the n-th triangle with integer sides i <= j <= k in a list of such triangles, the list being sorted by increasing size of R. Denominators are A331228.
%C A331227 Radii shared by more than one triangle are not removed. The first occurrence is for squared radius 64/15 at positions n = 10 and n = 11.
%F A331227 Squared radius of circumcircle of triangle with sides a, b, c:
%F A331227 R^2 = (a*b*c)^2 / (16*s*(s - a)*(s - b)*(s - c)) with s = (a + b + c)/2.
%e A331227 The first terms b(n) = a(n)/A331228(n) correspond to the following triangles (i, j, k):
%e A331227   b(1) = 1/3: (1,1,1),
%e A331227   b(2) = 16/15: (1,2,2),
%e A331227   b(3) = 4/3: (2,2,2),
%e A331227   b(4) = 16/7: (2,2,3) (obtuse triangle excluded in A331222),
%e A331227   b(5) = 81/35: (1,3,3),
%e A331227   b(6) = 81/32: (2,3,3),
%e A331227   b(7) = 3/1: (3,3,3),
%e A331227   b(8) = 81/20: (3,3,4),
%e A331227   b(9) = 256/63: (1,4,4),
%e A331227   b(10) = 64/15: (2,3,4), (obtuse)
%e A331227   b(11) = 64/15: (2,4,4).
%Y A331227 Cf. A331222, A331223, A331228.
%K A331227 nonn,frac
%O A331227 1,2
%A A331227 _Hugo Pfoertner_, Jan 12 2020