A149191 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, 0, -1), (-1, 0, 0), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 10, 38, 122, 488, 1710, 7087, 26321, 111541, 429981, 1852992, 7337801, 32021180, 129408800, 570358802, 2341953471, 10405274367, 43277165242, 193563780133, 813625097670, 3659544514239, 15519836602737, 70141510450253, 299727234321282, 1360257096588248, 5850780618278814

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[1 + i, j, k, -1 + n] + aux[1 + i, 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: A240382 A220198 A197051 * A149192 A032123 A149193

Adjacent sequences: A149188 A149189 A149190 * A149192 A149193 A149194

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved