49 lines
1.1 KiB
Markdown
49 lines
1.1 KiB
Markdown
---
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id: 5900f5181000cf542c51002a
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title: 'Problem 427: n-sequences'
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challengeType: 5
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forumTopicId: 302097
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dashedName: problem-427-n-sequences
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---
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# --description--
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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.
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For example, the sequence $S = \\{1, 5, 5, 10, 7, 7, 7, 2, 3, 7\\}$ is a 10-sequence.
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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.
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Let $f(n) = \sum L(S)$ for all $n$-sequences $S$.
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For example, $f(3) = 45$, $f(7) = 1\\,403\\,689$ and $f(11) = 481\\,496\\,895\\,121$.
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Find $f(7\\,500\\,000)\bmod 1\\,000\\,000\\,009$.
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# --hints--
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`nSequences()` should return `97138867`.
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```js
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assert.strictEqual(nSequences(), 97138867);
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```
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# --seed--
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## --seed-contents--
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```js
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function nSequences() {
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return true;
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}
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nSequences();
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```
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# --solutions--
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```js
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// solution required
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```
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