--description--

The Golomb's self-describing sequence ($G(n)$) is the only nondecreasing sequence of natural numbers such that $n$ appears exactly $G(n)$ times in the sequence. The values of $G(n)$ for the first few $n$ are

$$\begin{array}{c} n & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & \ldots \\ G(n) & 1 & 2 & 2 & 3 & 3 & 4 & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 6 & 6 & \ldots \end{array}$$

You are given that $G({10}^3) = 86$, $G({10}^6) = 6137$.

You are also given that $\sum G(n^3) = 153\,506\,976$ for $1 ≤ n < {10}^3$.

Find $\sum G(n^3)$ for $1 ≤ n < {10}^6$.

--hints--

golombsSequence() should return 56098610614277016.

assert.strictEqual(golombsSequence(), 56098610614277016);

--seed--

--seed-contents--

function golombsSequence() {

  return true;
}

golombsSequence();

--solutions--

// solution required