#### A000008 Make Change

```using System.Collections.Generic;
using System.Numerics;

namespace Algorithms.Sequences;

/// <summary>
///     <para>
///         Number of ways of making change for n cents using coins of 1, 2, 5, 10 cents.
///     </para>
///     <para>
///         OEIS: https://oeis.org/A000008.
///     </para>
/// </summary>
public class MakeChangeSequence : ISequence
{
/// <summary>
///     <para>
///         Gets sequence of number of ways of making change for n cents
///         using coins of 1, 2, 5, 10 cents.
///     </para>
///     <para>
///         Uses formula from OEIS page by Michael Somos
///         along with first 17 values to prevent index issues.
///     </para>
///     <para>
///         Formula:
///         a(n) = a(n-2) +a(n-5) - a(n-7) + a(n-10) - a(n-12) - a(n-15) + a(n-17) + 1.
///     </para>
/// </summary>
public IEnumerable<BigInteger> Sequence
{
get
{
var seed = new List<BigInteger>
{
1, 1, 2, 2, 3, 4, 5, 6, 7, 8,
11, 12, 15, 16, 19, 22, 25,
};
foreach (var value in seed)
{
yield return value;
}

for(var index = 17; ; index++)
{
BigInteger newValue = seed[index - 2] + seed[index - 5] - seed[index - 7]
+ seed[index - 10] - seed[index - 12] - seed[index - 15]
+ seed[index - 17] + 1;