A149473 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), (-1, 1, 1), (0, -1, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 55, 219, 947, 4124, 18509, 83805, 385192, 1784012, 8336935, 39189722, 185289101, 880043266, 4197296943, 20088159938, 96442832029, 464273089991, 2240451018858, 10835127441925, 52501963913485, 254843969483289, 1238967647764672, 6032102693466452, 29406664336282397, 143529821637417576

Offset

0,3

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, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A149470 A149471 A149472 * A365854 A188205 A149474

Adjacent sequences: A149470 A149471 A149472 * A149474 A149475 A149476

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved