A151106 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), (0, 0, 1), (0, 1, -1), (1, 0, 0), (1, 1, 0)}.

1, 3, 11, 44, 188, 834, 3796, 17595, 82652, 392296, 1876988, 9038428, 43750078, 212672939, 1037483310, 5076179561, 24898992612, 122392690133, 602735470493, 2972948379238, 14684093287089, 72615661668126, 359478469000610, 1781231772491187, 8833368751277994, 43837986172512587, 217700030074601239

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A394136 A026887 A389410 * A302186 A151107 A063018

Adjacent sequences: A151103 A151104 A151105 * A151107 A151108 A151109

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved