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

1,4

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Vladimir Letsko, Mathematical Marathon, problem 192 (in Russian).

Example

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

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;

Prog

(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

Crossrefs

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

Sequence in context: A164482 A359850 A349216 * A061866 A164476 A164466

Adjacent sequences: A247584 A247585 A247586 * A247588 A247589 A247590

Keyword

nonn

Author

Vladimir Letsko, Sep 20 2014

Status

approved