feat(6-kyu): kata/pell-numbers (#382)

Author: ParanoidUser

docs/README.md

@@ -1,7 +1,7 @@
 # Codewars Handbook ☕️🚀
 
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@@ -25,7 +25,7 @@ slug.
 
 | [1 kyu](/kata/1-kyu/index.md) | [2 kyu](/kata/2-kyu/index.md) | [3 kyu](/kata/3-kyu/index.md) | [4 kyu](/kata/4-kyu/index.md) | [5 kyu](/kata/5-kyu/index.md) | [6 kyu](/kata/6-kyu/index.md) | [7 kyu](/kata/7-kyu/index.md) | [8 kyu](/kata/8-kyu/index.md) | [beta](/kata/beta/index.md) | [retired](/kata/retired/index.md) |
 |:-----------------------------:|:-----------------------------:|:-----------------------------:|:-----------------------------:|:-----------------------------:|:-----------------------------:|:-----------------------------:|:-----------------------------:|:---------------------------:|:---------------------------------:|
-|               -               |               1               |               2               |              18               |              36               |              409              |              545              |              201              |             59              |                73                 |
+|               -               |               1               |               2               |              18               |              36               |              410              |              545              |              201              |             59              |                73                 |
 
 **Note:** The source code is written in Java 17 and may use language features that are incompatible
 with Java 8, 11.

kata/6-kyu/index.md

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 - [Password Maker](password-maker-1)
 - [Paths in the Grid](paths-in-the-grid)
 - [Peel the onion](peel-the-onion)
+- [Pell Numbers](pell-numbers)
 - [Pentabonacci](pentabonacci)
 - [Persistent Bugger](persistent-bugger)
 - [PhoneWords](phonewords-1)

kata/6-kyu/pell-numbers/README.md

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+# [Pell Numbers](https://www.codewars.com/kata/pell-numbers "https://www.codewars.com/kata/5818d00a559ff57a2f000082")
+
+The [Pell sequence](https://en.wikipedia.org/wiki/Pell_number) is the sequence of integers defined by the initial values
+
+```
+P(0) = 0, P(1) = 1
+```
+
+and the recurrence relation
+
+```
+P(n) = 2 * P(n-1) + P(n-2)
+```
+
+The first few values of `P(n)` are
+
+```
+0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, 33461, 80782, 195025, 470832, ...
+```
+
+## Task
+
+Your task is to write a method that returns `n`th Pell number

kata/6-kyu/pell-numbers/main/Solution.java

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+import java.math.BigInteger;
+
+import static java.math.BigInteger.ONE;
+import static java.math.BigInteger.TWO;
+import static java.util.stream.Stream.iterate;
+
+interface Solution {
+  static BigInteger pell(int n) {
+    return iterate(new BigInteger[]{ONE, TWO}, i -> new BigInteger[]{i[1], i[1].add(i[1]).add(i[0])})
+            .skip(n - 1L).findFirst().orElseThrow()[0];
+  }
+}

kata/6-kyu/pell-numbers/test/SolutionTest.java

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+import java.math.BigInteger;
+
+import org.junit.jupiter.api.Test;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+class SolutionTest {
+  @Test
+  void sample() {
+    assertEquals(BigInteger.ONE, Solution.pell(1));
+    assertEquals(BigInteger.TWO, Solution.pell(2));
+    assertEquals(BigInteger.valueOf(5), Solution.pell(3));
+    assertEquals(BigInteger.valueOf(12), Solution.pell(4));
+  }
+}