#### A002717 Matchstick Triangle Arrangement

```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++;
}
}
}
}
```