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A070104
Number of integer triangles with perimeter n and relatively prime side lengths which are obtuse and scalene.
3
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 2, 2, 3, 1, 4, 3, 6, 2, 7, 4, 8, 4, 8, 6, 10, 6, 12, 8, 14, 8, 16, 11, 18, 11, 17, 14, 21, 12, 25, 18, 25, 15, 30, 19, 32, 20, 32, 25, 38, 23, 40, 28, 41, 28, 47, 31, 51, 34, 46, 40, 55, 35, 61, 44, 58, 41, 68
OFFSET
1,13
LINKS
MAPLE
f:= proc(n) local a, b, q, bmin, bmax, t;
t:= 0;
for a from 1 to n/3 do
if n::even then bmin:= max(a+1, n/2-a+1) else bmin:= max(a+1, (n+1)/2-a) fi;
q:= (n^2-2*n*a)/(2*(n-a));
if q::integer then bmax:= min((n-a)/2, q-1) else bmax:= min((n-a)/2, floor(q)) fi;
t:= t + nops(select(b -> igcd(a, b, n-a-b) = 1, [$bmin .. bmax]))
od;
t
end proc:
map(f, [$1..100]); # Robert Israel, Jul 26 2024
KEYWORD
nonn,look
AUTHOR
Reinhard Zumkeller, May 05 2002
STATUS
approved