A150785 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, 0, 1), (1, 0, 1), (1, 1, -1), (1, 1, 0)}

1, 2, 8, 30, 135, 579, 2723, 12339, 59277, 276665, 1345269, 6393287, 31322030, 150637188, 741700919, 3596682654, 17770927067, 86693084805, 429420886016, 2104274543789, 10442645460273, 51347690040441, 255178100991149, 1258116115806969, 6259192509479481, 30926062538141649, 153991023855675944

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150782 A150783 A150784 * A036723 A150786 A150787

Adjacent sequences: A150782 A150783 A150784 * A150786 A150787 A150788

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved