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using System.Collections.Generic;
using System.Numerics;
namespace Algorithms.Sequences;
/// <summary>
/// <para>
/// Sequence of binomial coefficients.
/// </para>
/// <para>
/// Wikipedia: https://en.wikipedia.org/wiki/Binomial_coefficient.
/// </para>
/// <para>
/// OEIS: http://oeis.org/A007318.
/// </para>
/// </summary>
public class BinomialSequence : ISequence
{
/// <summary>
/// Gets sequence of binomial coefficients.
/// </summary>
public IEnumerable<BigInteger> Sequence
{
get
{
var i = 0;
while (true)
{
var row = GenerateRow(i);
foreach (var coefficient in row)
{
yield return coefficient;
}
i++;
}
}
}
private static BigInteger BinomialCoefficient(long n, long k)
{
if (k == 0 || k == n)
{
return new BigInteger(1);
}
if (n < 0)
{
return new BigInteger(0);
}
return BinomialCoefficient(n - 1, k) + BinomialCoefficient(n - 1, k - 1);
}
private static IEnumerable<BigInteger> GenerateRow(long n)
{
long k = 0;
while (k <= n)
{
yield return BinomialCoefficient(n, k);
k++;
}
}
}
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