A151175 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, 0, 0), (1, 1, 0), (1, 1, 1)}

1, 3, 12, 49, 219, 971, 4517, 20771, 98450, 461981, 2213354, 10519245, 50753596, 243307767, 1179762984, 5690972110, 27696647862, 134229569535, 655129908566, 3186566575192, 15587994181738, 76039623155226, 372662021788428, 1822155305407466, 8944059110331015, 43817771192888596, 215363155240618719

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 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: A151173 A301456 A151174 * A151176 A151177 A344419

Adjacent sequences: A151172 A151173 A151174 * A151176 A151177 A151178

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved