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%I #10 Jan 22 2020 14:14:19
%S 0,1,3,7,14,22,34,47,67,91,117,148,187,231,281,334,400,469,548,631,
%T 727,830,943,1062,1202,1339,1490,1657,1833,2024,2226,2434,2662,2905,
%U 3155,3427,3712,4014,4321,4653,5005,5362,5749,6141,6558,6994,7440,7911,8408,8917
%N a(n) = number of triangles with integer sides i <= j <= k with diameter of circumcircle <= n.
%e The diameter of the n-th circumcircle in the sorted list is D(n) = 2*sqrt(A331227(n)/A331228(n)). The list of diameters, rounded to 10^-4, starts: {1.1547, 2.0656, 2.3094, 3.0237, 3.0426, 3.1820, 3.4641, 4.0249, 4.0316, 4.1312, 4.1312, 4.3149, 4.6188, 5.0000, 5.0252, ...}.
%e a(1) = 0: 0 circles with D <= 1,
%e a(2) = 1: 1 circle (D = 1.1547) with 1 < D <= 2,
%e a(3) = 3: a(2) + 2 circles (D = 2.0656, 2.3094) with 2 < D <= 3,
%e a(4) = 7: a(3) + 4 circles (D = 3.02, 3.04, 3.18, 3.46) with 3 < D <= 4,
%e a(5) = 14: a(4) + 7 circles (D = 4.0249, ..., 5) with 4 < D <= 5.
%Y Cf. A331227, A331228, A331229.
%K nonn,more
%O 1,3
%A _Hugo Pfoertner_, Jan 13 2020
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