A150171 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, 0, 1), (0, -1, 1), (0, 1, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 6, 20, 76, 299, 1246, 5291, 23180, 102766, 464418, 2115781, 9761718, 45299638, 212074088, 997141485, 4718451470, 22402002642, 106868910086, 511158778549, 2453901475690, 11805274313163, 56957327738323, 275279817557115, 1333530890867209, 6469275458458120, 31443031209732966, 153009244617227957

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, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150169 A083691 A150170 * A263902 A150172 A263903

Adjacent sequences: A150168 A150169 A150170 * A150172 A150173 A150174

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved