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

namespace Algorithms.Sequences
{
    /// <summary>
    ///     <para>
    ///         Catalan numbers: C[n+1] = (2*(2*n+1)*C[n])/(n+2).
    ///     </para>
    ///     <para>
    ///         Wikipedia: https://en.wikipedia.org/wiki/Catalan_number.
    ///     </para>
    ///     <para>
    ///         OEIS:http://oeis.org/A000108.
    ///     </para>
    /// </summary>
    public class CatalanSequence : ISequence
    {
        /// <summary>
        ///     Gets sequence of Catalan numbers.
        /// </summary>
        public IEnumerable<BigInteger> Sequence
        {
            get
            {
                // initialize the first element (1) and define it's enumerator (0)
                var catalan = new BigInteger(1);
                var n = 0;
                while (true)
                {
                    yield return catalan;
                    catalan = (2 * (2 * n + 1) * catalan) / (n + 2);
                    n++;
                }
            }
        }
    }
}