A070104 Number of integer triangles with perimeter n and relatively prime side lengths which are obtuse and scalene.

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

Author

Reinhard Zumkeller, May 05 2002

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• R. Zumkeller, Integer-sided triangles

Crossrefs

Cf. A070080, A070081, A070082, A070101, A051493, A005044, A070102, A024156, A070084, A070131.

Programs

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