A149151 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, 1), (-1, 0, 1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 9, 38, 117, 473, 1627, 6781, 24491, 103183, 385432, 1643302, 6283473, 26949455, 105057704, 452722835, 1789652210, 7743159255, 30968509503, 134376514919, 542440479936, 2360077322154, 9602440029186, 41863048009064, 171470991401328, 748932471713277, 3085313428804808, 13496157140944834

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, k, -1 + 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, 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: A149148 A149149 A149150 * A149152 A149153 A101529

Adjacent sequences: A149148 A149149 A149150 * A149152 A149153 A149154

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved