A331243 a(n) = number of triangles with integer sides i <= j <= k with diameter of enclosing circle <= n.

0, 1, 4, 8, 16, 26, 39, 56, 79, 106, 138, 175, 221, 272, 331, 397, 471, 555, 648, 750

Offset

1,3

Comments

The enclosing circle differs from the circumcircle by limiting the diameter to the longest side k for obtuse triangles, i.e., those with i^2 + j^2 < k^2.

Links

Table of n, a(n) for n=1..20.

Example

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.

Crossrefs

Cf. A331229, A331240, A331242, A331244, A331245, A331246.

Sequence in context: A050470 A138501 A096296 * A180861 A353316 A068936

Adjacent sequences: A331240 A331241 A331242 * A331244 A331245 A331246

Keyword

nonn,more

Author

Hugo Pfoertner, Jan 20 2020

Status

approved