freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-427-n-sequences.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f5181000cf542c51002a	Problem 427: n-sequences	5	302097	problem-427-n-sequences

--description--

A sequence of integers S = \\{s_i\\} is called an $n$-sequence if it has n elements and each element s_i satisfies 1 ≤ s_i ≤ n. Thus there are n^n distinct $n$-sequences in total.

For example, the sequence S = \\{1, 5, 5, 10, 7, 7, 7, 2, 3, 7\\} is a 10-sequence.

For any sequence S, let L(S) be the length of the longest contiguous subsequence of S with the same value. For example, for the given sequence S above, L(S) = 3, because of the three consecutive 7's.

Let f(n) = \sum L(S) for all $n$-sequences S.

For example, f(3) = 45, f(7) = 1\\,403\\,689 and f(11) = 481\\,496\\,895\\,121.

Find f(7\\,500\\,000)\bmod 1\\,000\\,000\\,009.

--hints--

nSequences() should return 97138867.

assert.strictEqual(nSequences(), 97138867);

--seed--

--seed-contents--

function nSequences() {

  return true;
}

nSequences();

--solutions--

// solution required