A149437 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, 0, 0), (0, -1, 0), (0, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 46, 173, 687, 2761, 11324, 47305, 200512, 858136, 3705606, 16136055, 70762084, 312140489, 1384023100, 6166060651, 27588011071, 123900214425, 558332251754, 2523850427923, 11441252563467, 52001415898658, 236914399797222, 1081742883431362, 4949323510305669, 22687867098425114

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A149435 A149436 A087440 * A149438 A151448 A218667

Adjacent sequences: A149434 A149435 A149436 * A149438 A149439 A149440

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved