A149767 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, 0, 0), (1, -1, 0), (1, -1, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 19, 75, 303, 1297, 5557, 24261, 106399, 472551, 2107115, 9466037, 42670843, 193357621, 878695095, 4008039183, 18326746125, 84037953711, 386156408739, 1778381839873, 8204508712775, 37920438844591, 175530699463693, 813755080675841, 3777510322216653, 17558169592824157, 81705648375517987

Offset

0,3

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, j, 1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A098913 A126392 A206373 * A149768 A149769 A149770

Adjacent sequences: A149764 A149765 A149766 * A149768 A149769 A149770

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved