A331257 Numerator of squared radius of inscribed circle of the n-th triangle with integer sides in the list given by A316841. Denominators are A331258.

1, 3, 1, 9, 5, 1, 3, 5, 4, 7, 3, 45, 4, 25, 21, 1, 75, 9, 2, 63, 12, 25, 35, 9, 27, 8, 7, 9, 11, 5, 27, 2, 175, 3, 49, 3, 3, 147, 11, 5, 135, 8, 245, 13, 3, 99, 20, 225, 18, 49, 63, 16, 55, 5, 189, 16, 39, 4, 165, 3, 15, 48, 15, 7, 117, 12, 275, 45, 441, 16

Offset

1,2

Links

Table of n, a(n) for n=1..70.

Formula

Radius of inscribed circle of a triangle with sides (a,b,c):

rho(a,b,c) = sqrt((s - a)*(s - b)*(s - c)/s) with s = (a + b + c)/2.

Example

   n i (A316843)
   | | j (A316844)
   | | | k (A316845)
   | | | |  a(n) this sequence
   | | | |  |  A331258(n)
   | | | |  |  |  rho = sqrt(a(n)/A331258(n))
   1 1 1 1  1 12  0.28868
   2 2 2 1  3 20  0.38730
   3 2 2 2  1  3  0.57735
   4 3 2 2  9 28  0.56695
   5 3 3 1  5 28  0.42258
   6 3 3 2  1  2  0.70711
   7 3 3 3  3  4  0.86603
   8 4 3 2  5 12  0.64550
   9 4 3 3  4  5  0.89443
  10 4 4 1  7 36  0.44096
  11 4 4 2  3  5  0.77460
  12 4 4 3 45 44  1.01130
  13 4 4 4  4  3  1.15470
  14 5 3 3 25 44  0.75378
  15 5 4 2 21 44  0.69085
  16 5 4 3  1  1  1.00000

Prog

(PARI)
rh2(a, b, c)={my(s=(a+b+c)/2); (s-a)*(s-b)*(s-c)/s};
for(i=1, 8, for(j=1, i, for(k=1, j, if(j+k>i, print1(numerator(rh2(i, j, k)), ", ")))))

Crossrefs

Cf. A316841, A316843, A316844, A316845, A331258.

Sequence in context: A136159 A371746 A005533 * A112626 A050155 A270236

Adjacent sequences: A331254 A331255 A331256 * A331258 A331259 A331260

Keyword

nonn,frac

Author

Hugo Pfoertner, Jan 26 2020

Status

approved