A149716 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, 0, 1), (0, 1, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 17, 71, 297, 1301, 5723, 25809, 117441, 539487, 2497203, 11641745, 54540565, 256723897, 1213481451, 5755777471, 27383682569, 130648021511, 624862345197, 2995106483281, 14385115772833, 69216330388613, 333594136086683, 1610226943470809, 7783322584383833, 37670523046306671, 182538800744367371

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, 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149713 A149714 A149715 * A324800 A146577 A211405

Adjacent sequences: A149713 A149714 A149715 * A149717 A149718 A149719

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved