A149776 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), (0, 1, -1), (1, -1, 0), (1, 1, 1)}.

1, 1, 5, 19, 79, 337, 1471, 6583, 30005, 138107, 642385, 3006461, 14166593, 67079683, 319162579, 1524296757, 7305132769, 35112906661, 169209219035, 817320823289, 3955891659183, 19182488863913, 93171981471417, 453234904283099, 2207784673155213, 10767956886477083, 52578503928246405, 257003334368999857

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, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + 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: A149774 A160702 A149775 * A149777 A149778 A163609

Adjacent sequences: A149773 A149774 A149775 * A149777 A149778 A149779

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved