count-sorted-vowel-strings

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Algorithms

Given an integer <code>n</code>, return the number of strings of length <code>n</code> that consist only of vowels (<code>a</code>, <code>e</code>, <code>i</code>, <code>o</code>, <code>u</code>) and are lexicographically sorted.

A string <code>s</code> is lexicographically sorted if for all valid <code>i</code>, <code>s[i]</code> is the same as or comes before <code>s[i+1]</code> in the alphabet.

&nbsp;
Example 1:

<pre>
Input: n = 1
Output: 5
Explanation: The 5 sorted strings that consist of vowels only are <code>[&quot;a&quot;,&quot;e&quot;,&quot;i&quot;,&quot;o&quot;,&quot;u&quot;].</code>
</pre>

Example 2:

<pre>
Input: n = 2
Output: 15
Explanation: The 15 sorted strings that consist of vowels only are
[&quot;aa&quot;,&quot;ae&quot;,&quot;ai&quot;,&quot;ao&quot;,&quot;au&quot;,&quot;ee&quot;,&quot;ei&quot;,&quot;eo&quot;,&quot;eu&quot;,&quot;ii&quot;,&quot;io&quot;,&quot;iu&quot;,&quot;oo&quot;,&quot;ou&quot;,&quot;uu&quot;].
Note that &quot;ea&quot; is not a valid string since &#39;e&#39; comes after &#39;a&#39; in the alphabet.
</pre>

Example 3:

<pre>
Input: n = 33
Output: 66045
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 50</code>&nbsp;</li>
</ul>