A070203 Number of scalene integer triangles with perimeter n having integral inradius.

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

Offset: 1

Author

Reinhard Zumkeller, May 05 2002

Keywords

• nonn

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

Crossrefs

Cf. A024153, A005044.

Programs

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