A149208 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, -1, 0), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 10, 40, 131, 543, 1995, 8492, 33265, 144245, 588503, 2586676, 10852579, 48195518, 206354186, 923882538, 4016849256, 18102778754, 79653690932, 360933654486, 1603372701367, 7298673862103, 32676073002920, 149326831866216, 672858765696468, 3085329699710324, 13977902597587443

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + 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: A149206 A149207 A156798 * A149209 A053792 A032121

Adjacent sequences: A149205 A149206 A149207 * A149209 A149210 A149211

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved