A149230 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), (-1, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 10, 46, 149, 690, 2497, 11744, 45062, 214536, 853892, 4098631, 16729527, 80801096, 335978483, 1630298162, 6876922865, 33488217825, 142893840268, 697795200077, 3005761292354, 14711115274258, 63872848725319, 313190405733228, 1369038458461978, 6723217549168217, 29561165849692203

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, -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: A149227 A149228 A149229 * A115327 A233395 A197664

Adjacent sequences: A149227 A149228 A149229 * A149231 A149232 A149233

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved