A148107 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, -1, 0), (-1, 1, 0), (0, 0, 1), (1, -1, 1), (1, 0, -1)}.

1, 1, 2, 4, 10, 27, 84, 265, 892, 3078, 10917, 39683, 147762, 559640, 2154331, 8416964, 33261595, 132862775, 536061253, 2182072592, 8952086612, 37000546739, 153950290800, 644361566782, 2712078227312, 11474353274885, 48776461977010, 208261335853889, 892909478125003, 3842953777938297

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A275428 A202058 A346999 * A148108 A057786 A262496

Adjacent sequences: A148104 A148105 A148106 * A148108 A148109 A148110

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved