A247587 Number of obtuse triangles with integer sides at most n.

0, 0, 1, 2, 4, 8, 13, 20, 30, 42, 57, 74, 95, 120, 149, 182, 219, 261, 309, 362, 420, 485, 556, 632, 715, 806, 906, 1012, 1125, 1247, 1377, 1517, 1666, 1824, 1993, 2170, 2358, 2555, 2765, 2986

Offset: 1

Author

Vladimir Letsko, Sep 20 2014

Keywords

• nonn

Examples

			a(4) = 2 because there are 2 obtuse triangles with integer sides less than or equal to 4: (2,2,3); (2,3,4).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Vladimir Letsko, Mathematical Marathon, problem 192 (in Russian).

Crossrefs

Cf. A002623, A224921, A247586, A247588, A247589.

Programs

Maple

tr_o:=proc(n) local a, b, c, t, d; t:=0:
  for a to n do
  for b from a to n do
  for c from b to min(a+b-1, n) do
  d:=a^2+b^2-c^2:
  if d<0 then t:=t+1 fi
  od od od;
  [n, t]; end;

PARI

a(n)=sum(a=2,n-1,sum(b=a,n-1,max(0,min(n,a+b-1)-sqrtint(a^2+b^2)))) \\ Charles R Greathouse IV, Sep 20 2014

PARI

obtuse(n)=sum(a=2,n-1, max(0, sqrtint(n^2-1-a^2)-max(a,n-a+1)+1))
s=0; vector(100,n, s+=obtuse(n)) \\ Charles R Greathouse IV, Sep 20 2014