A151026 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, 0, 1), (1, -1, 0), (1, 1, 0), (1, 1, 1)}.

1, 2, 10, 40, 192, 840, 4136, 19072, 93984, 443200, 2197056, 10529408, 52254080, 252754560, 1257233536, 6125430784, 30490513920, 149263315968, 743819838464, 3655479169024, 18224641949696, 89813644283904, 448049879896064, 2213201659002880, 11044272618651648, 54650659023355904, 272818438753746944

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + 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: A333799 A030534 A335601 * A151027 A188325 A151028

Adjacent sequences: A151023 A151024 A151025 * A151027 A151028 A151029

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved