<section id="description">
Let <var>a</var>, <var>b</var> and <var>c</var> be positive numbers.
Let W, X, Y, Z be four collinear points where |WX| = <var>a</var>, |XY| = <var>b</var>, |YZ| = <var>c</var> and |WZ| = <var>a</var> + <var>b</var> + <var>c</var>.
Let Cin be the circle having the diameter XY.
Let Cout be the circle having the diameter WZ.The triplet (<var>a</var>, <var>b</var>, <var>c</var>) is called a necklace triplet if you can place <var>k</var> ≥ 3 distinct circles C1, C2, ..., C<var>k</var> such that:
<ul><li>C<var>i</var> has no common interior points with any C<var>j</var> for 1 ≤ <var>i</var>, <var>j</var> ≤ <var>k</var> and <var>i</var> ≠ <var>j</var>,</li><li>C<var>i</var> is tangent to both Cin and Cout for 1 ≤ <var>i</var> ≤ <var>k</var>,</li><li>C<var>i</var> is tangent to C<var>i</var>+1 for 1 ≤ <var>i</var> &#x3C; <var>k</var>, and</li><li>C<var>k</var> is tangent to C1.</li></ul>
For example, (5, 5, 5) and (4, 3, 21) are necklace triplets, while it can be shown that (2, 2, 5) is not.<img src="https://projecteuler.net/project/images/p428_necklace.png" alt="a visual reresentation of a necklace triplet">
Let T(<var>n</var>) be the number of necklace triplets (<var>a</var>, <var>b</var>, <var>c</var>) such that <var>a</var>, <var>b</var> and <var>c</var> are positive integers, and <var>b</var> ≤ <var>n</var>.
For example, T(1) = 9, T(20) = 732 and T(3000) = 438106.
Find T(1 000 000 000).
</section>

function necklace(n) {
  // Good luck!
  return true;
}

necklace(1000000000)


index

Задача 428: Ожерелье кругов

Problem 428: Necklace of Circles

<code>necklace(1000000000)</code> should return 747215561862.