A149264 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, 0, -1), (1, 1, 1)}.

1, 1, 4, 11, 40, 128, 490, 1647, 6460, 22668, 88980, 320904, 1267096, 4635894, 18391702, 68175937, 270692796, 1013765698, 4032287792, 15203817018, 60568746766, 229786861594, 915830459954, 3492539188184, 13929844315396, 53327961184274, 212838079458018, 817696688446820, 3264339179583992

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, -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: A149261 A149262 A149263 * A264331 A243760 A149265

Adjacent sequences: A149261 A149262 A149263 * A149265 A149266 A149267

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved