cp's OEIS Frontend

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

%I A070203 #19 Feb 16 2025 08:32:46
%S A070203 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,
%T A070203 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,
%U A070203 0,2,0,2,0,0,0,1,0,1,0,2,0,0,0,8,0,0,0,1,0,3
%N A070203 Number of scalene integer triangles with perimeter n having integral inradius.
%C A070203 a(n) = A070201(n) - A070204(n).
%H A070203 Seiichi Manyama, <a href="/A070203/b070203.txt">Table of n, a(n) for n = 1..5000</a>
%H A070203 Mohammad K. Azarian, <a href="http://www.jstor.org/stable/25678790">Solution to Problem S125: Circumradius and Inradius</a>, Math Horizons, Vol. 16, Issue 2, November 2008, p. 32.
%H A070203 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Incircle.html">Incircle</a>.
%H A070203 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ScaleneTriangle.html">Scalene Triangle</a>.
%H A070203 R. Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>
%o A070203 (Ruby)
%o A070203 def A(n)
%o A070203   cnt = 0
%o A070203   (1..n / 3).each{|a|
%o A070203     (a + 1..(n - a) / 2).each{|b|
%o A070203       c = n - a - b
%o A070203       if a + b > c && b < c
%o A070203         s = n / 2r
%o A070203         t = (s - a) * (s - b) * (s - c) / s
%o A070203         if t.denominator == 1
%o A070203           t = t.to_i
%o A070203           cnt += 1 if Math.sqrt(t).to_i ** 2 == t
%o A070203         end
%o A070203       end
%o A070203     }
%o A070203   }
%o A070203   cnt
%o A070203 end
%o A070203 def A070203(n)
%o A070203   (1..n).map{|i| A(i)}
%o A070203 end
%o A070203 p A070203(100) # _Seiichi Manyama_, Oct 07 2017
%Y A070203 Cf. A024153, A005044.
%K A070203 nonn
%O A070203 1,36
%A A070203 _Reinhard Zumkeller_, May 05 2002