A150966 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, 0, 1), (1, 1, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 35, 169, 738, 3629, 16682, 82647, 390196, 1940421, 9306773, 46377697, 224704740, 1121102225, 5469493627, 27308595009, 133886659448, 668792536841, 3290820689923, 16443320070637, 81132737454840, 405479153513625, 2004938623970498, 10021491503813491, 49636023934102274, 248123929732377761

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, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A150963 A150964 A150965 * A185034 A185234 A357202

Adjacent sequences: A150963 A150964 A150965 * A150967 A150968 A150969

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved