--description--

For two positive integers $a$ and $b$, the Ulam sequence $U(a,b)$ is defined by ${U{(a,b)}_1} = a$, ${U{(a,b)}_2} = b$ and for $k > 2$, ${U{(a,b)}_k}$ is the smallest integer greater than ${U{(a,b)}_{(k-1)}}$ which can be written in exactly one way as the sum of two distinct previous members of $U(a,b)$.

For example, the sequence $U(1,2)$ begins with

$$1, 2, 3 = 1 + 2, 4 = 1 + 3, 6 = 2 + 4, 8 = 2 + 6, 11 = 3 + 8$$

5 does not belong to it because $5 = 1 + 4 = 2 + 3$ has two representations as the sum of two previous members, likewise $7 = 1 + 6 = 3 + 4$.

Find $\sum {U(2, 2n + 1)_k}$ for $2 ≤ n ≤ 10$, where $k = {10}^{11}$.

--hints--

ulamSequences() should return 3916160068885.

assert.strictEqual(ulamSequences(), 3916160068885);

--seed--

--seed-contents--

function ulamSequences() {

  return true;
}

ulamSequences();

--solutions--

// solution required