A331224 Numerator of squared radius of circumscribed circle of a triangle with integer sides i <= j <= k, such that the number of triangles with this radius sets a new record. Denominators are A331225.

1, 64, 49, 1024, 2025, 4096, 25600, 2401, 7744, 148225, 8281, 2073600, 123904, 774400, 3705625

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Formula

Squared radius of circumcircle of triangle with sides a, b, c:

R^2 = (a*b*c)^2 / (16*s*(s - a)*(s - b)*(s - c)) with s = (a + b + c)/2.

Example

Correspondence of the first terms b(n) = a(n)/A331225(n) with triangles (i, j, k):
b(1) = 1/3: (1,1,1), start with 1 = A331226(1) triangle.
b(2) = 64/15: (2,3,4), (2,4,4) is the first occurrence of 2 = A331226(2) triangles with identical R.
b(3) = 49/3: (3,5,7), (3,7,8), (5,7,8), (7,7,7) is the first occurrence of more triangles with identical R than the previous record 2, new record is 4 = A331226(3).
b(4) = 1024/15: (5,8,12), (5,14,16), (8,8,14), (8,12,16), (8,16,16), (12,14,16) is the first occurrence of more triangles with identical R than the previous record 4, new record is 6 = A331226(4).

Crossrefs

Cf. A331040, A331041, A331225, A331226, A331227, A331228.

Sequence in context: A169639 A252486 A188828 * A123994 A248770 A272297

Adjacent sequences: A331221 A331222 A331223 * A331225 A331226 A331227

Keyword

nonn,frac,more

Author

Hugo Pfoertner, Jan 14 2020

Status

approved