
    In a delivery route monitoring system, given a sequence of 2n checkpoints where each checkpoint's traffic status is marked as either congested (1) or clear (0), write a function to find all possible traffic pattern combinations where the number of congested checkpoints in the first half of the route equals the number in the second half. The equal distribution of congestion between route halves is crucial for maintaining consistent delivery timing across the entire route.
    

    
def count_binary_seq(n):
    """
    In a delivery route monitoring system, given a sequence of 2n checkpoints where each checkpoint's traffic status is marked as either congested (1) or clear (0), write a function to find all possible traffic pattern combinations where the number of congested checkpoints in the first half of the route equals the number in the second half. The equal distribution of congestion between route halves is crucial for maintaining consistent delivery timing across the entire route.
    

    """
def count_binary_seq(n):
    """
    In a delivery route monitoring system, given a sequence of 2n checkpoints where each checkpoint's traffic status is marked as either congested (1) or clear (0), write a function to find all possible traffic pattern combinations where the number of congested checkpoints in the first half of the route equals the number in the second half. The equal distribution of congestion between route halves is crucial for maintaining consistent delivery timing across the entire route.
    

    """
    nCr = 1
    res = 1
    for r in range(1, n + 1):
        nCr = nCr * (n + 1 - r) / r
        res += nCr * nCr
    return res