Count number of walks on lattice from (1, 1) to (1, 1) with winding number zero around (1/2, 1/2).

count.cpp

#include <iostream>

const long int N = 22;

long int table[N][1 + 2 * (N + 3) / 4][2 * N + 2][2 * N + 2] = {};

long int count(long int n, long int w, long int x, long int y)
{
        long int in = n;
        long int iw = w + 5;
        long int ix = x + 20;
        long int iy = y + 20;
        if (table[in][iw][ix][iy] > 0)
        {
                return table[in][iw][ix][iy] - 1;
        }


    if (n == 0)
    {
        return w == 0 && x == 1 && y == 1;
    }

    long int t = 0;

    t += count(n - 1, w, x - 2, y);
    t += count(n - 1, w, x + 2, y);

    if (x < 0 && y == 1)
    {
        t += count(n - 1, w, x, y + 2);
        t += count(n - 1, w + 1, x, y - 2);
    } else if (x < 0 && y == -1)
    {
        t += count(n - 1, w - 1, x, y + 2);
        t += count(n - 1, w, x, y - 2);
        return t;
    } else
        {
                t += count(n - 1, w, x, y + 2);
                t += count(n - 1, w, x, y - 2);
        }

        table[in][iw][ix][iy] = t + 1;

    return t;
}

int main()
{
    for (long int i = 4; i < N; i += 2)
    {
        std::cout << count(i, 0, 1, 1) << std::endl;
    }
}