A149164 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, -1), (-1, 1, 1), (1, -1, 0), (1, 1, 0)}

1, 1, 4, 9, 40, 119, 547, 1853, 8660, 31519, 149037, 568401, 2710708, 10688967, 51292180, 207333529, 999662616, 4118904097, 19934948055, 83399651303, 404890953262, 1715089952957, 8347765182386, 35727736510393, 174270194092570, 752395213601045, 3676723076166319, 15992803135093301

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A149161 A149162 A149163 * A238420 A302179 A354738

Adjacent sequences: A149161 A149162 A149163 * A149165 A149166 A149167

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved