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

1,36

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: A208575 A355037 A365832 * A070201 A070138 A024153

Adjacent sequences: A070200 A070201 A070202 * A070204 A070205 A070206

Keyword

nonn

Author

Reinhard Zumkeller, May 05 2002

Status

approved