A148979 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, 1), (1, -1, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 32, 112, 416, 1595, 6274, 25167, 102555, 423339, 1768311, 7458501, 31731885, 136027943, 587011854, 2548351515, 11122561784, 48780963600, 214886096297, 950408168978, 4218983830646, 18792082175472, 83964867542325, 376248603204020, 1690509753133442, 7614571890623423, 34378422957641746

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[i, 1 + 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: A202143 A330464 A148978 * A148980 A148981 A148982

Adjacent sequences: A148976 A148977 A148978 * A148980 A148981 A148982

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved