A331229 a(n) = number of triangles with integer sides i <= j <= k with radius of circumcircle <= n.

1, 7, 22, 47, 91, 148, 231, 334, 469, 631, 830, 1062, 1339, 1657, 2024, 2434, 2905, 3427, 4014, 4653, 5362, 6141, 6994, 7911, 8917, 10000, 11169, 12425, 13774, 15211, 16743, 18381, 20133, 21975, 23929, 25998, 28185, 30482, 32906, 35449, 38137, 40935, 43884, 46954

Offset

1,2

Links

Table of n, a(n) for n=1..44.

Example

The radius of the m-th circumcircle in the sorted list is R(m) = sqrt(A331227(m)/A331228(m)). The list of radii, rounded to 10^-4, starts: {0.57735, 1.0328, 1.1547, 1.5119, 1.5213, 1.5910, 1.7321, 2.0125, 2.0158, 2.0656, 2.0656, 2.1574, 2.3094, 2.5000, 2.5126, 2.5516, 2.5621, 2.6207, 2.6318, 2.7136, 2.7277, 2.8868, 3.0067, ...}.
a(1) = 1: 1 circle (R = 0.57735) with R <= 1,
a(2) = 7: a(1) + 6 circles (R = 1.0328, 1.1547, 1.5119, 1.5213, 1.5910, 1.7321) with 1 < R <= 2,
a(3) = 22: a(2) + 15 circles (R = 2.0125, 2.0158, 2.0656, 2.0656, 2.1574, 2.3094, 2.5000, 2.5126, 2.5516, 2.5621, 2.6207, 2.6318, 2.7136, 2.7277, 2.8868) with 2 < R <= 3.

Crossrefs

Cf. A331227, A331228.

Bisection of A331240 (n even).

Sequence in context: A132438 A010001 A197059 * A299283 A244243 A223833

Adjacent sequences: A331226 A331227 A331228 * A331230 A331231 A331232

Keyword

nonn

Author

Hugo Pfoertner, Jan 13 2020

Status

approved