以下是用C#實現二叉樹中路徑和的計算方法：

using System;

public class TreeNode
{
    public int val;
    public TreeNode left;
    public TreeNode right;
    public TreeNode(int value = 0, TreeNode leftChild = null, TreeNode rightChild = null)
    {
        val = value;
        left = leftChild;
        right = rightChild;
    }
}

public class BinaryTree
{
    public int PathSum(TreeNode root, int sum)
    {
        if (root == null)
        {
            return 0;
        }

        return PathSumFrom(root, sum) + PathSum(root.left, sum) + PathSum(root.right, sum);
    }

    private int PathSumFrom(TreeNode node, int sum)
    {
        if (node == null)
        {
            return 0;
        }

        int count = 0;
        if (node.val == sum)
        {
            count++;
        }

        count += PathSumFrom(node.left, sum - node.val);
        count += PathSumFrom(node.right, sum - node.val);

        return count;
    }
}

class Program
{
    static void Main()
    {
        TreeNode root = new TreeNode(10);
        root.left = new TreeNode(5);
        root.right = new TreeNode(-3);
        root.left.left = new TreeNode(3);
        root.left.right = new TreeNode(2);
        root.right.right = new TreeNode(11);
        root.left.left.left = new TreeNode(3);
        root.left.left.right = new TreeNode(-2);
        root.left.right.right = new TreeNode(1);

        BinaryTree tree = new BinaryTree();
        int sum = 8;
        int result = tree.PathSum(root, sum);

        Console.WriteLine("Number of paths with sum " + sum + ": " + result);
    }
}

在上面的代碼中，我們定義了一個TreeNode類來表示二叉樹中的節點，以及一個BinaryTree類來計算二叉樹中路徑和等于給定值的路徑數量。在BinaryTree類中，我們使用遞歸的方法來遍歷二叉樹，并計算路徑和等于給定值的路徑數量。在Main方法中，我們創建了一個二叉樹，并計算路徑和等于8的路徑數量。