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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS 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 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: A091579 A136159 A005533 * A112626 A050155 A270236 Adjacent sequences:  A331254 A331255 A331256 * A331258 A331259 A331260 KEYWORD nonn,frac AUTHOR Hugo Pfoertner, Jan 26 2020 STATUS approved

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Last modified January 22 02:46 EST 2022. Contains 350481 sequences. (Running on oeis4.)