A149804 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, 1), (-1, 1, 1), (1, -1, 0), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 19, 89, 379, 1823, 8197, 40045, 185935, 914769, 4333969, 21414917, 102774477, 509373665, 2466218669, 12248424895, 59682477719, 296839596157, 1453286699987, 7235830952857, 35553973216713, 177163737383945, 872967747931467, 4352639615034501, 21495504532627355, 107228704066746623

Offset

0,3

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

Crossrefs

Sequence in context: A149802 A149803 A259204 * A340994 A301702 A296162

Adjacent sequences: A149801 A149802 A149803 * A149805 A149806 A149807

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved