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A070203 Number of scalene integer triangles with perimeter n having integral inradius. 4
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, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 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) = A070201(n) - A070204(n).

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, Scalene Triangle.

R. Zumkeller, Integer-sided triangles

PROG

(Ruby)

def A(n)

  cnt = 0

  (1..n / 3).each{|a|

    (a + 1..(n - a) / 2).each{|b|

      c = n - a - b

      if a + b > c && 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 A070203(n)

  (1..n).map{|i| A(i)}

end

p A070203(100) # Seiichi Manyama, Oct 07 2017

CROSSREFS

Cf. A024153, A005044.

Sequence in context: A333146 A135767 A208575 * A070201 A070138 A024153

Adjacent sequences:  A070200 A070201 A070202 * A070204 A070205 A070206

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 05 2002

STATUS

approved

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Last modified June 1 13:11 EDT 2020. Contains 334762 sequences. (Running on oeis4.)