A151157 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, 1, -1), (0, 1, 0), (1, 0, 0), (1, 1, 1)}

1, 3, 11, 47, 209, 961, 4512, 21421, 102808, 496807, 2413594, 11779861, 57683735, 283272704, 1394366123, 6876523311, 33968458501, 168026808732, 832125985706, 4125174186124, 20467951716101, 101633767892268, 505001251563912, 2510738271490330, 12489242911825944, 62154228935090911, 309444661727216957

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A151154 A151155 A151156 * A151158 A055731 A151159

Adjacent sequences: A151154 A151155 A151156 * A151158 A151159 A151160

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved