The following figure shows a walk of length 6:
[asy]
unitsize(20);
for (int x = -5; x <= 5; ++x)
for (int y = 0; y <= 5; ++y)
dot((x, y));
label("O", (0, 0), S);
draw((0, 0) -- (1, 0) -- (1, 1) -- (0, 1) -- (-1, 1) -- (-1, 2) -- (-1, 3));
[/asy]
This walk has three interesting properties:[*] It starts at the origin, labelled O.
[*] Each step is 1 unit north, east, or west. There are no south steps.
[*] The walk never comes back to a point it has been to.Let's call a walk with these three properties a northern walk. There are 3 northern walks of length 1 and 7 northern walks of length 2. How many northern walks of length 6 are there? linear algebramatrixalgebrapolynomial