A150044 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, -1, 0), (-1, -1, 1), (0, 1, 0), (1, 1, 0)}.

1, 2, 6, 18, 60, 205, 732, 2667, 9944, 37635, 144510, 561066, 2200371, 8701862, 34671959, 139048957, 560902064, 2274347907, 9265281738, 37904895120, 155669154825, 641556300312, 2652566214507, 10999819260498, 45739849085085, 190680566875170, 796788140682092, 3336830737459782

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, -1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A048117 A048118 A004113 * A108531 A150045 A191280

Adjacent sequences: A150041 A150042 A150043 * A150045 A150046 A150047

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved