A150889 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), (0, -1, 0), (0, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 8, 34, 150, 682, 3174, 14970, 71340, 342710, 1656644, 8046426, 39237846, 191962322, 941663210, 4629658186, 22805288372, 112519961104, 555947186900, 2750201653992, 13619337222924, 67507071559382, 334885832641942, 1662481553291334, 8258372677711584, 41046761708327586, 204119269616094816

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, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[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: A151829 A026387 A085362 * A150890 A150891 A074606

Adjacent sequences: A150886 A150887 A150888 * A150890 A150891 A150892

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved