freeCodeCamp/problem-319-bounded-sequences.english.md at 92377cf71af628cb5ea6b28ff7d6fa66a9b52449

mrugesh 22afc2a0ca feat(learn): python certification projects (#38216 )

Co-authored-by: Oliver Eyton-Williams <ojeytonwilliams@gmail.com>
Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com>
Co-authored-by: Beau Carnes <beaucarnes@gmail.com>

2020-05-27 13:19:08 +05:30

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id, challengeType, isHidden, title, forumTopicId

id	challengeType	isHidden	title	forumTopicId
5900f4ab1000cf542c50ffbe	5	false	Problem 319: Bounded Sequences	301975

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.

Instructions

Tests

tests:
  - text: <code>euler319()</code> should return 268457129.
    testString: assert.strictEqual(euler319(), 268457129);

Challenge Seed

function euler319() {
  // Good luck!
  return true;
}

euler319();

Solution

// solution required

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