A150156 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), (0, 0, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 20, 74, 292, 1198, 5028, 21622, 94588, 419610, 1878692, 8496032, 38730284, 177775372, 820162304, 3804035456, 17724013876, 82916301210, 389148105248, 1832406667400, 8653542367792, 40975173604142, 194451410866520, 924852778993384, 4407708855232164, 21045901379183460, 100652903635533476

Offset

0,2

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, k, -1 + n] + aux[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: A150154 A006850 A150155 * A150157 A371712 A145867

Adjacent sequences: A150153 A150154 A150155 * A150157 A150158 A150159

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved