A149479 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), (-1, 1, 1), (1, -1, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 57, 224, 1038, 4459, 21206, 95450, 460768, 2133473, 10395594, 49032011, 240409450, 1148482686, 5655779024, 27268079722, 134709037376, 653917834101, 3238092590185, 15800643148860, 78382843357317, 384029211313430, 1907725906035345, 9376714816549434, 46631525727999251, 229790507773596674

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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}]

Crossrefs

Sequence in context: A316117 A149477 A149478 * A149480 A151481 A283612

Adjacent sequences: A149476 A149477 A149478 * A149480 A149481 A149482

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved