A151234 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, 1), (0, 1, 1), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 3, 13, 59, 283, 1359, 6675, 32727, 162095, 802141, 3988263, 19825449, 98780051, 492183055, 2455358493, 12250068089, 61159025611, 305364267749, 1525285941063, 7619299421445, 38070181020027, 190230440111887, 950694213535645, 4751400412277505, 23748934255071507, 118708556168222291

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A151321 A151232 A151233 * A330799 A367057 A317776

Adjacent sequences: A151231 A151232 A151233 * A151235 A151236 A151237

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved