A151253 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (0, 0, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0)}.

1, 4, 19, 91, 445, 2188, 10819, 53644, 266581, 1326646, 6609307, 32953033, 164397313, 820521562, 4096733707, 20459928259, 102203137741, 510621146326, 2551485015379, 12750737780587, 63725988599425, 318514790389294, 1592093707211299, 7958459733327676, 39783873348471745, 198883941062337328

Offset: 0

Author

Manuel Kauers, Nov 18 2008

Keywords

• nonn
• walk

Comments

Binomial transform of A151162. - Philippe Deléham, Feb 03 2009

Links

• A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Programs

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]