A150595 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), (0, 1, -1), (1, 0, 0), (1, 1, -1), (1, 1, 1)}.

1, 2, 7, 27, 107, 446, 1881, 8092, 35281, 155332, 689317, 3077837, 13822709, 62370888, 282595987, 1284860299, 5859939781, 26800809480, 122881479385, 564677253173, 2600094786295, 11994498454736, 55425906674189, 256520478250400, 1188929043764117, 5517825227850990, 25640044127268883, 119281290605788607

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[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: A360149 A192417 A150594 * A150596 A026726 A150597

Adjacent sequences: A150592 A150593 A150594 * A150596 A150597 A150598

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved