--description--

Consider the set $S(r)$ of points ($x$,$y$) with integer coordinates satisfying $|x| + |y| ≤ r$.

Let $O$ be the point (0,0) and $C$ the point ($\frac{r}{4}$,$\frac{r}{4}$).

Let $N(r)$ be the number of points $B$ in $S(r)$, so that the triangle $OBC$ has an obtuse angle, i.e. the largest angle $α$ satisfies $90°<α<180°$.

So, for example, $N(4)=24$ and $N(8)=100$.

What is $N(1\,000\,000\,000)$?

--hints--

obtuseAngledTriangles() should return 1598174770174689500.

assert.strictEqual(obtuseAngledTriangles(), 1598174770174689500);

--seed--

--seed-contents--

function obtuseAngledTriangles() {

  return true;
}

obtuseAngledTriangles();

--solutions--

// solution required