A150300 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), (-1, 0, 0), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 21, 80, 275, 1120, 4164, 17627, 68636, 297325, 1194403, 5261790, 21631711, 96502081, 403736439, 1818348174, 7712720923, 35000405956, 150124914344, 685486436315, 2967502084569, 13619251406030, 59418422131252, 273872899297569, 1202825082289681, 5564479952269571, 24579592893740449

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, 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: A060900 A305850 A151289 * A150301 A150302 A150303

Adjacent sequences: A150297 A150298 A150299 * A150301 A150302 A150303

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved