A149218 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, 0), (0, 0, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 10, 42, 145, 602, 2388, 10042, 42498, 183049, 799499, 3524763, 15688373, 70431199, 317977943, 1446357299, 6607070514, 30349207627, 139970939560, 648077550792, 3011857721135, 14039719950122, 65651502348997, 307805927487748, 1446796565404772, 6816563009764308, 32183644379465378

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A149215 A149216 A149217 * A149219 A361938 A222475

Adjacent sequences: A149215 A149216 A149217 * A149219 A149220 A149221

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved