A149168 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, 0, 1)}

1, 1, 4, 9, 42, 130, 590, 2065, 9590, 36246, 169302, 662508, 3151302, 12716418, 60766134, 249975297, 1204668894, 5046138526, 24387184250, 103327379584, 502209024746, 2152035376998, 10480335520954, 45276651995848, 221246448525258, 963621977231330, 4715103886462790, 20657384214505530

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, 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: A070761 A149166 A149167 * A149169 A138544 A219287

Adjacent sequences: A149165 A149166 A149167 * A149169 A149170 A149171

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved