A149266 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), (-1, 0, 0), (0, -1, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 11, 40, 145, 557, 2204, 8878, 36670, 153158, 649421, 2779083, 12009927, 52301065, 229322103, 1011602788, 4485941698, 19989047298, 89445085086, 401786301272, 1811068535817, 8189394966213, 37138317913733, 168865708226573, 769695000793202, 3516190063129191, 16096483440690982

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, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A264331 A243760 A149265 * A149267 A149268 A214142

Adjacent sequences: A149263 A149264 A149265 * A149267 A149268 A149269

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved