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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
OFFSET
1,36
COMMENTS
a(n) = A070201(n) - A070204(n).
LINKS
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.
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
Sequence in context: A208575 A355037 A365832 * A070201 A070138 A024153
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 05 2002
STATUS
approved