A149755 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, -1), (1, 1, 1)}.

1, 1, 5, 17, 83, 333, 1645, 7195, 35733, 162789, 810585, 3784801, 18875529, 89559607, 447055739, 2144687329, 10711656671, 51798394103, 258799786711, 1258926493065, 6291422329465, 30743907572127, 153664965152667, 753582461828893, 3766970533585897, 18525963698745311, 92613362991207555

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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, 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: A149752 A149753 A149754 * A365878 A363163 A002020

Adjacent sequences: A149752 A149753 A149754 * A149756 A149757 A149758

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved