A150042 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, -1), (-1, 0, 1), (-1, 1, 0), (0, 0, 1), (1, 0, 0)}.

1, 2, 6, 18, 58, 198, 699, 2555, 9496, 35858, 137357, 532718, 2088905, 8261370, 32902004, 131899705, 531966574, 2157304467, 8790642741, 35967722498, 147723568543, 608879673427, 2517980169752, 10444486214272, 43440861244434, 181131270913433, 757027164305121, 3170993736654692

Offset

0,2

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, k, -1 + n] + aux[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, 1 + 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: A085139 A150041 A190790 * A351279 A036675 A227373

Adjacent sequences: A150039 A150040 A150041 * A150043 A150044 A150045

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved