login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A070201 Number of integer triangles with perimeter n having integral inradius. 9
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 0, 2, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 8, 0, 0, 0, 1, 0, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,36

COMMENTS

a(n) = #{k | A070083(k) = n and A070200(k) = exact inradius};

a(n) = A070203(n) + A070204(n);

a(n) = A070205(n) + A070206(n) + A024155(n);

a(odd) = 0.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Mohammad K. Azarian, Solution to Problem S125: Circumradius and Inradius, Math Horizons, Vol. 16, Issue 2, November 2008, p. 32.

Eric Weisstein's World of Mathematics, Incircle.

Eric Weisstein's World of Mathematics, Heron's Formula.

R. Zumkeller, Integer-sided triangles

EXAMPLE

a(36)=2, as there are two integer triangles with integer inradius having perimeter=32:

First: [A070080(368), A070081(368), A070082(368)] = [9,10,17], for s = A070083(368)/2 = (9+10+17)/2 = 18: inradius = sqrt((s-9)*(s-10)*(s-17)/s) = sqrt(9*8*1/18) = sqrt(4) = 2; therefore A070200(368) = 2.

2nd: [A070080(370), A070081(370), A070082(370)] = [9,12,15], for s = A070083(370)/2 = (9+12+15)/2 = 18: inradius = sqrt((s-9)*(s-12)*(s-15)/s) = sqrt(9*6*3/18) = sqrt(9) = 3; therefore A070200(370) = 3.

PROG

(Ruby)

def A(n)

  cnt = 0

  (1..n / 3).each{|a|

    (a..(n - a) / 2).each{|b|

      c = n - a - b

      if a + b > c

        s = n / 2r

        t = (s - a) * (s - b) * (s - c) / s

        if t.denominator == 1

          t = t.to_i

          cnt += 1 if Math.sqrt(t).to_i ** 2 == t

        end

      end

    }

  }

  cnt

end

def A070201(n)

  (1..n).map{|i| A(i)}

end

p A070201(100) # Seiichi Manyama, Oct 06 2017

CROSSREFS

Cf. A070209, A070202, A070208, A005044, A070140.

Sequence in context: A135767 A208575 A070203 * A070138 A024153 A079127

Adjacent sequences:  A070198 A070199 A070200 * A070202 A070203 A070204

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 05 2002

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 April 5 20:24 EDT 2020. Contains 333260 sequences. (Running on oeis4.)