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

Author

Hugo Pfoertner, Jan 26 2020

Keywords

• nonn
• frac

Examples

			   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
		

Crossrefs

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

Programs

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)), ", ")))))

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.