A150157 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, 0, 1), (1, -1, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 20, 74, 292, 1202, 5106, 22185, 98124, 440191, 1997709, 9153957, 42286652, 196697066, 920385559, 4328900377, 20452147695, 97010623252, 461766013148, 2204856757852, 10557294423169, 50677691551001, 243819054493735, 1175475321726869, 5677725595782312, 27471347112562462, 133127597567879393

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + 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: A006850 A150155 A150156 * A371712 A145867 A188144

Adjacent sequences: A150154 A150155 A150156 * A150158 A150159 A150160

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved