A150378 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, 0), (1, -1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 23, 96, 370, 1582, 6521, 28643, 122638, 546792, 2394446, 10792173, 48021728, 218179960, 981883990, 4488678934, 20373041373, 93593834773, 427623466487, 1972421243699, 9059494556338, 41927367649728, 193403822529562, 897622038677730, 4155362828482880, 19333035594712891, 89767486969505492

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[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150375 A150376 A150377 * A150379 A150380 A150381

Adjacent sequences: A150375 A150376 A150377 * A150379 A150380 A150381

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved