A149496 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, -1, 0), (-1, 0, -1), (0, -1, -1), (1, 1, 1)}.

1, 1, 5, 9, 45, 109, 497, 1505, 6133, 21789, 82533, 321777, 1194945, 4811085, 18219585, 73076577, 286306473, 1134972601, 4568099273, 18063724073, 73541366101, 293534062209, 1194924730629, 4838269689497, 19642019715565, 80442812392417, 326934305905229, 1345821122024457, 5501463899445453

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[i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A220518 A145031 A121724 * A149497 A149498 A149499

Adjacent sequences: A149493 A149494 A149495 * A149497 A149498 A149499

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved