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

--description--

Let x_1, x_2, \ldots, x_n be a sequence of length n such that:

x_1 = 2
for all 1 < i ≤ n : x_{i - 1} < x_i
for all i and j with 1 ≤ i, j ≤ n : {(x_i)}^j < {(x_j + 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({10}^{10}) and give your answer modulo 10^9.

--hints--

boundedSequences() should return 268457129.

assert.strictEqual(boundedSequences(), 268457129);

--seed--

--seed-contents--

function boundedSequences() {

  return true;
}

boundedSequences();

--solutions--

// solution required

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