A148337 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, -1, 0), (-1, 1, 1), (0, 0, -1), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 5, 14, 47, 143, 473, 1629, 5605, 20435, 73465, 269905, 1008533, 3767243, 14375250, 54928164, 211709811, 822476562, 3204543546, 12593678660, 49651915597, 196804253006, 783229067840, 3127723687414, 12544032531028, 50446880736135, 203642910438415, 824114620749925, 3344745342125251

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A107268 A231211 A006216 * A149899 A149900 A149901

Adjacent sequences: A148334 A148335 A148336 * A148338 A148339 A148340

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved