A215577 Number of nonintersecting (or self-avoiding) rook paths joining opposite corner cells of an n X n X n grid, avoiding cells that are not on the surface.

1, 18, 340812, 1553113040

Offset: 1

Author

Alex Ratushnyak, Aug 16 2012

Keywords

• nonn
• walk
• more

Comments

When n<3 there are n^3 cells available, otherwise n^3 - (n-2)^3.

The length of the step is 1. The length of the path varies.

Crossrefs

Cf. A007764, A059783.

Programs

C

#include     // GCC -O3
char grid[4][4][4];
long long SIZE;
long long calc_ways(long long x, long long y, long long z) {
    long long n;
    if (grid[x][y][z]) return 0;
    if (x+y+z==SIZE*3-3) return 1;
    grid[x][y][z]=1;
    n=0;
    if (x>0)        n =calc_ways(x-1,y,z);  // go left
    if (x0)        n+=calc_ways(x,y-1,z);  // down
    if (y0)        n+=calc_ways(x,y,z-1);  // level down
    if (z