How many path options are there for a 4x4 field, if you can walk right, down, right-down?

Question

Mathematics

Is it considered according to the formula and where to dig?
And if there are 5?6?7 fields?
upd fixed a couple of typos

Answer 1

I myself faced a similar problem, if I understood you correctly.
habrahabr.ru/qa/6563/
And here is a link where everything is described in detail
mathworld.wolfram.com/Self-AvoidingWalk.html
As a result, there is no general formula (
But this is if your task matches the way I understood you.

Answer 2

Try to solve the problem using dynamic programming. It may even work in general terms.

Answer 3

#include <iostream>
#include <cstdlib>
using namespace std;

#define ROWS 4
#define COLS 4

int f(int row, int col) {
    if(row == 0 && col == 0)
        return 1;
    int result = 0;
    if(row > 0)
        result += f(row - 1, col);
    if(row > 0 && col > 0)
        result += f(row - 1, col - 1);
    if(col > 0)
        result += f(row, col - 1);
    return result;
}
int main() {
    cout << f(ROWS - 1,COLS - 1);
    system("pause"); 
}

Here is the solution to the problem.
With 4x4 there will be 63

Answer 4

To clarify the conditions:

I think the author means this.