cp's OEIS Frontend

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.

%I A331257 #11 May 31 2024 10:36:03
%S A331257 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,
%T A331257 5,27,2,175,3,49,3,3,147,11,5,135,8,245,13,3,99,20,225,18,49,63,16,55,
%U A331257 5,189,16,39,4,165,3,15,48,15,7,117,12,275,45,441,16
%N 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.
%F A331257 Radius of inscribed circle of a triangle with sides (a,b,c):
%F A331257 rho(a,b,c) = sqrt((s - a)*(s - b)*(s - c)/s) with s = (a + b + c)/2.
%e A331257    n i (A316843)
%e A331257    | | j (A316844)
%e A331257    | | | k (A316845)
%e A331257    | | | |  a(n) this sequence
%e A331257    | | | |  |  A331258(n)
%e A331257    | | | |  |  |  rho = sqrt(a(n)/A331258(n))
%e A331257    1 1 1 1  1 12  0.28868
%e A331257    2 2 2 1  3 20  0.38730
%e A331257    3 2 2 2  1  3  0.57735
%e A331257    4 3 2 2  9 28  0.56695
%e A331257    5 3 3 1  5 28  0.42258
%e A331257    6 3 3 2  1  2  0.70711
%e A331257    7 3 3 3  3  4  0.86603
%e A331257    8 4 3 2  5 12  0.64550
%e A331257    9 4 3 3  4  5  0.89443
%e A331257   10 4 4 1  7 36  0.44096
%e A331257   11 4 4 2  3  5  0.77460
%e A331257   12 4 4 3 45 44  1.01130
%e A331257   13 4 4 4  4  3  1.15470
%e A331257   14 5 3 3 25 44  0.75378
%e A331257   15 5 4 2 21 44  0.69085
%e A331257   16 5 4 3  1  1  1.00000
%o A331257 (PARI)
%o A331257 rh2(a, b, c)={my(s=(a+b+c)/2); (s-a)*(s-b)*(s-c)/s};
%o A331257 for(i=1, 8, for(j=1, i, for(k=1, j, if(j+k>i, print1(numerator(rh2(i, j, k)), ", ")))))
%Y A331257 Cf. A316841, A316843, A316844, A316845, A331258.
%K A331257 nonn,frac
%O A331257 1,2
%A A331257 _Hugo Pfoertner_, Jan 26 2020