A150713 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), (0, 0, -1), (0, 1, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 8, 27, 124, 503, 2339, 10145, 48142, 216689, 1038060, 4785186, 23084148, 108070026, 523987765, 2480766805, 12073222580, 57632297111, 281311616872, 1351376339808, 6611757818228, 31919938473737, 156472662648119, 758425209359445, 3723783575960449, 18108045615852210, 89028860865463775

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[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: A150710 A150711 A150712 * A383974 A276940 A287204

Adjacent sequences: A150710 A150711 A150712 * A150714 A150715 A150716

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved