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A070203 Number of scalene integer triangles with perimeter n having integral inradius. 4

%I #18 Oct 07 2017 10:11:46

%S 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 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 0,2,0,2,0,0,0,1,0,1,0,2,0,0,0,8,0,0,0,1,0,3

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

%C a(n) = A070201(n) - A070204(n).

%H Seiichi Manyama, <a href="/A070203/b070203.txt">Table of n, a(n) for n = 1..5000</a>

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Incircle.html">Incircle</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ScaleneTriangle.html">Scalene Triangle</a>.

%H R. Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>

%o (Ruby)

%o def A(n)

%o cnt = 0

%o (1..n / 3).each{|a|

%o (a + 1..(n - a) / 2).each{|b|

%o c = n - a - b

%o if a + b > c && b < c

%o s = n / 2r

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

%o if t.denominator == 1

%o t = t.to_i

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

%o end

%o end

%o }

%o }

%o cnt

%o end

%o def A070203(n)

%o (1..n).map{|i| A(i)}

%o end

%o p A070203(100) # _Seiichi Manyama_, Oct 07 2017

%Y Cf. A024153, A005044.

%K nonn

%O 1,36

%A _Reinhard Zumkeller_, May 05 2002

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)