A151232 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, 0), (0, 1, 1), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 3, 13, 59, 279, 1341, 6529, 31981, 157601, 778977, 3861201, 19173317, 95347081, 474671533, 2365049859, 11791810723, 58822652725, 293556016993, 1465487556179, 7317966766907, 36550573297817, 182589335006819, 912264053437413, 4558459999510109, 22780286787593095, 113850845864419591

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A151231 A299502 A151321 * A151233 A151234 A330799

Adjacent sequences: A151229 A151230 A151231 * A151233 A151234 A151235

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved