49 lines
1018 B
Markdown
49 lines
1018 B
Markdown
---
|
|
id: 5900f5181000cf542c51002a
|
|
title: 'Problem 427: n-sequences'
|
|
challengeType: 5
|
|
forumTopicId: 302097
|
|
dashedName: problem-427-n-sequences
|
|
---
|
|
|
|
# --description--
|
|
|
|
A sequence of integers S = {si} is called an n-sequence if it has n elements and each element si satisfies 1 ≤ si ≤ n. Thus there are nn 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) = ∑ L(S) for all n-sequences S.
|
|
|
|
For example, f(3) = 45, f(7) = 1403689 and f(11) = 481496895121.
|
|
|
|
Find f(7 500 000) mod 1 000 000 009.
|
|
|
|
# --hints--
|
|
|
|
`euler427()` should return 97138867.
|
|
|
|
```js
|
|
assert.strictEqual(euler427(), 97138867);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function euler427() {
|
|
|
|
return true;
|
|
}
|
|
|
|
euler427();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|