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id	title	challengeType	forumTopicId	dashedName
5900f4ab1000cf542c50ffbe	Problem 319: Bounded Sequences	5	301975	problem-319-bounded-sequences

--description--

Let x1, x2,..., xn be a sequence of length n such that:

x1 = 2

for all 1 < i ≤ n : xi-1 < xi

for all i and j with 1 ≤ i, j ≤ n : (xi) j < (xj + 1)i

There are only five such sequences of length 2, namely: {2,4}, {2,5}, {2,6}, {2,7} and {2,8}. There are 293 such sequences of length 5; three examples are given below: {2,5,11,25,55}, {2,6,14,36,88}, {2,8,22,64,181}.

Let t(n) denote the number of such sequences of length n. You are given that t(10) = 86195 and t(20) = 5227991891.

Find t(1010) and give your answer modulo 109.

--hints--

euler319() should return 268457129.

assert.strictEqual(euler319(), 268457129);

--seed--

--seed-contents--

function euler319() {

  return true;
}

euler319();

--solutions--

// solution required

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