A331240
a(n) = number of triangles with integer sides i <= j <= k with diameter of circumcircle <= n.
Original entry on oeis.org
0, 1, 3, 7, 14, 22, 34, 47, 67, 91, 117, 148, 187, 231, 281, 334, 400, 469, 548, 631, 727, 830, 943, 1062, 1202, 1339, 1490, 1657, 1833, 2024, 2226, 2434, 2662, 2905, 3155, 3427, 3712, 4014, 4321, 4653, 5005, 5362, 5749, 6141, 6558, 6994, 7440, 7911, 8408, 8917
Offset: 1
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, ...}.
a(1) = 0: 0 circles with D <= 1,
a(2) = 1: 1 circle (D = 1.1547) with 1 < D <= 2,
a(3) = 3: a(2) + 2 circles (D = 2.0656, 2.3094) with 2 < D <= 3,
a(4) = 7: a(3) + 4 circles (D = 3.02, 3.04, 3.18, 3.46) with 3 < D <= 4,
a(5) = 14: a(4) + 7 circles (D = 4.0249, ..., 5) with 4 < D <= 5.
A331242
a(n) = number of triangles with integer sides i <= j <= k with radius of enclosing circle <= n.
Original entry on oeis.org
1, 8, 26, 56, 106, 175, 272, 397, 555, 750
Offset: 1
The list of radii of the n-th enclosing circle, rounded to 10^-4, starts: {0.57735, 1.0328, 1.1547, 1.5000, 1.5213, 1.5910, 1.7321, 2.0000, 2.0125, 2.0158, 2.0656, 2.1574, 2.3094, 2.5000, 2.5000, 2.5000, 2.5126, 2.5516, 2.5621, 2.6207, 2.7277, 2.8868, 3.0000, 3.0000, 3.0000, 3.0000, 3.0105, ...}.
a(1) = 1: 1 circle (R = 0.57735) with R <= 1,
a(2) = 8: a(1) + 7 circles (R = 1.0328, 1.1547, 1.5000, 1.5213, 1.5910, 1.7321, 2.0000) with 1 < R <= 2,
a(3) = 26: a(2) + 18 circles (R = 2.0125, 2.0158, 2.0656, 2.1574, 2.3094, 2.5000, 2.5000, 2.5000, 2.5126, 2.5516, 2.5621, 2.6207, 2.7277, 2.8868, 3.0000, 3.0000, 3.0000, 3.0000) with 2 < R <= 3.
A331243
a(n) = number of triangles with integer sides i <= j <= k with diameter of enclosing circle <= n.
Original entry on oeis.org
0, 1, 4, 8, 16, 26, 39, 56, 79, 106, 138, 175, 221, 272, 331, 397, 471, 555, 648, 750
Offset: 1
The sorted list of diameters D(n), rounded to 10^-4, starts: {1.1547, 2.0656, 2.3094, 3.0000, 3.0426, 3.1820, 3.4641, 4.0000, 4.0249, 4.0316, 4.1312, 4.3149, 4.6188, 5.0000, 5.0000, 5.0000, 5.0252, ...}.
a(1) = 0: 0 circles with D <= 1,
a(2) = 1: 1 circle (D = 1.1547) with 1 < D <= 2,
a(3) = 4: a(2) + 3 circles (D = 2.0656, 2.3094, 3.0000) with 2 < D <= 3,
a(4) = 8: a(3) + 4 circles (D = 3.04, 3.18, 3.46, 4.00) with 3 < D <= 4,
a(5) = 16: a(4) + 8 circles (D = 4.0249, ..., 5, 5, 5) with 4 < D <= 5.
Showing 1-3 of 3 results.
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