GetBiggestSum.cs

using System;

namespace CSharpPractice
{
    class Program
    {
        static void Main(string[] args)
        {
            int[,] arr = new int[2, 4]
            {
                { 13, -2, 3, 2 },
                { -1,  2, 4, 7 }
            };

            int[,] mem = new int[2, 4];
            Console.WriteLine(GetBiggestSum(ref arr, ref mem, 1, 3));
        }

        private static int GetBiggestSum(ref int[,] arr, ref int[,] mem, int i, int j)
        {
            if (mem[i, j] > 0)
            {
                return mem[i, j];
            }

            if (i == 0 & j == 0)
            {
                return mem[i, j] = arr[i, j];
            }
            else if (i == 0)
            {
                return mem[i, j] = arr[i, j] + GetBiggestSum(ref arr, ref mem, i, j - 1);
            }
            else if (j == 0)
            {
                return mem[i, j] = arr[i, j] + GetBiggestSum(ref arr, ref mem, i - 1, j);
            }

            return mem[i, j] = arr[i, j]
                + Math.Max(GetBiggestSum(ref arr, ref mem, i - 1, j - 1),
                Math.Max(GetBiggestSum(ref arr, ref mem, i - 1, j), GetBiggestSum(ref arr, ref mem, i, j - 1)));
        }
    }
}