--description--

A horizontal row comprising of $2n + 1$ squares has $n$ red counters placed at one end and $n$ blue counters at the other end, being separated by a single empty square in the center. For example, when $n = 3$.

A counter can move from one square to the next (slide) or can jump over another counter (hop) as long as the square next to that counter is unoccupied.

Let $M(n)$ represent the minimum number of moves/actions to completely reverse the positions of the colored counters; that is, move all the red counters to the right and all the blue counters to the left.

It can be verified $M(3) = 15$, which also happens to be a triangle number.

If we create a sequence based on the values of n for which $M(n)$ is a triangle number then the first five terms would be: 1, 3, 10, 22, and 63, and their sum would be 99.

Find the sum of the first forty terms of this sequence.

--hints--

swappingCounters() should return 2470433131948040.

assert.strictEqual(swappingCounters(), 2470433131948040);

--seed--

--seed-contents--

function swappingCounters() {

  return true;
}

swappingCounters();

--solutions--

// solution required