login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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