Add Sequence A002717 (TheAlgorithms#354)

Author: RichardVasquez

Algorithms.Tests/Sequences/MatchstickTriangleSequenceTests.cs

@@ -0,0 +1,28 @@
+using System.Linq;
+using System.Numerics;
+using Algorithms.Sequences;
+using FluentAssertions;
+using NUnit.Framework;
+
+namespace Algorithms.Tests.Sequences;
+
+[TestFixture]
+public static class MatchstickTriangleSequenceTests
+{
+    private static BigInteger[] TestList = {
+                                               0, 1, 5, 13, 27, 48, 78, 118, 170, 235, 315, 411, 525, 658,
+                                               812, 988, 1188, 1413, 1665, 1945, 2255, 2596, 2970, 3378,
+                                               3822, 4303, 4823, 5383, 5985, 6630, 7320, 8056, 8840, 9673,
+                                               10557, 11493, 12483, 13528, 14630, 15790, 17010, 18291,
+                                               19635, 21043, 22517,
+                                           };
+    /// <summary>
+    ///     This test uses the list values provided from http://oeis.org/A002717/list.
+    /// </summary>
+    [Test]
+    public static void TestOeisList()
+    {
+        var sequence = new MatchstickTriangleSequence().Sequence.Take(TestList.Length);
+        sequence.SequenceEqual(TestList).Should().BeTrue();
+    }
+}

Algorithms/Sequences/MatchstickTriangleSequence.cs

@@ -0,0 +1,71 @@
+using System;
+using System.Collections.Generic;
+using System.Numerics;
+
+namespace Algorithms.Sequences;
+
+/// <summary>
+///     <para>
+///         Sequence of number of triangles in triangular matchstick arrangement of side n for n>=0.
+///     </para>
+///     <para>
+///         M. E. Larsen, The eternal triangle – a history of a counting problem, College Math. J., 20 (1989), 370-392.
+///         https://web.math.ku.dk/~mel/mel.pdf.
+///     </para>
+///     <para>
+///         OEIS: http://oeis.org/A002717.
+///     </para>
+/// </summary>
+public class MatchstickTriangleSequence : ISequence
+{
+    /// <summary>
+    ///     <para>
+    ///         Gets number of triangles contained in an triangular arrangement of matchsticks of side length n.
+    ///     </para>
+    ///     <para>
+    ///         This also counts the subset of smaller triangles contained within the arrangement.
+    ///     </para>
+    ///     <para>
+    ///         Based on the PDF referenced above, the sequence is derived from step 8, using the resulting equation
+    ///         of f(n) = (n(n+2)(2n+1) -(delta)(n)) / 8.  Using BigInteger values, we can effectively remove
+    ///         (delta)(n) from the previous by using integer division instead.
+    ///     </para>
+    ///     <para>
+    ///         Examples follow.
+    /// <pre>
+    ///   .
+    ///  / \   This contains 1 triangle of size 1.
+    /// .---.
+    ///
+    ///     .
+    ///    / \     This contains 4 triangles of size 1.
+    ///   .---.    This contains 1 triangle of size 2.
+    ///  / \ / \   This contains 5 triangles total.
+    /// .---.---.
+    ///
+    ///       .
+    ///      / \      This contains 9 triangles of size 1.
+    ///     .---.     This contains 3 triangles of size 2.
+    ///    / \ / \    This contains 1 triangles of size 3.
+    ///   .---.---.
+    ///  / \ / \ / \  This contains 13 triangles total.
+    /// .---.---.---.
+    /// </pre>
+    ///     </para>
+    /// </summary>
+    public IEnumerable<BigInteger> Sequence
+    {
+        get
+        {
+            var index = BigInteger.Zero;
+            var eight = new BigInteger(8);
+            while (true)
+            {
+                var temp = index * (index + 2) * (index * 2 + 1);
+                var result = BigInteger.Divide(temp, eight);
+                yield return result;
+                index++;
+            }
+        }
+    }
+}

README.md

@@ -144,6 +144,7 @@ find more than one implementation for the same objective but using different alg
     * [A001462 Golomb's](./Algorithms/Sequences/GolombsSequence.cs)
     * [A001478 Negative Integers](./Algorithms/Sequences/NegativeIntegersSequence.cs)
     * [A002110 Primorial Numbers](./Algorithms/Sequences/PrimorialNumbersSequence.cs)
+    * [A002717 Matchstick Triangle Arrangement](./Algorithms/Sequences/MatchstickTriangleSequence.cs)
     * [A005132 Recaman's](./Algorithms/Sequences/RecamansSequence.cs)
     * [A006577 Number of '3n+1' steps to reach 1](./Algorithms/Sequences/ThreeNPlusOneStepsSequence.cs)
     * [A006862 Euclid Numbers](./Algorithms/Sequences/EuclidNumbersSequence.cs)