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id	challengeType	title
5900f5241000cf542c510037	5	Problem 440: GCD and Tiling

Description

We want to tile a board of length n and height 1 completely, with either 1 × 2 blocks or 1 × 1 blocks with a single decimal digit on top:

For example, here are some of the ways to tile a board of length n = 8:

Let T(n) be the number of ways to tile a board of length n as described above.

For example, T(1) = 10 and T(2) = 101.

Let S(L) be the triple sum ∑a,b,c gcd(T(ca), T(cb)) for 1 ≤ a, b, c ≤ L. For example: S(2) = 10444 S(3) = 1292115238446807016106539989 S(4) mod 987 898 789 = 670616280.

Find S(2000) mod 987 898 789.

Instructions

Tests

tests:
  - text: <code>euler440()</code> should return 970746056.
    testString: assert.strictEqual(euler440(), 970746056, '<code>euler440()</code> should return 970746056.');

Challenge Seed

function euler440() {
  // Good luck!
  return true;
}

euler440();

Solution

// solution required

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