OFFSET
1,2
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
KEYWORD
nonn,frac
AUTHOR
Hugo Pfoertner, Jan 26 2020
STATUS
approved