A148019 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, 0), (0, 0, 1), (0, 1, -1), (1, -1, -1)}.

1, 1, 2, 3, 8, 17, 46, 120, 355, 1032, 3100, 9340, 29696, 95081, 313347, 1029034, 3432205, 11592025, 39779168, 137877429, 481249138, 1686693258, 5964861195, 21272314918, 76492455917, 276544510969, 1003517401394, 3658674178950, 13417837913677, 49490455637968, 183410344857840, 681873034580703, 2542965407836124

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A148016 A148017 A148018 * A148020 A148021 A148022

Adjacent sequences: A148016 A148017 A148018 * A148020 A148021 A148022

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved