A148152 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), (-1, 0, 0), (0, 0, 1), (0, 1, -1), (1, -1, 1)}.

1, 1, 2, 4, 11, 30, 93, 297, 971, 3338, 11610, 41667, 151870, 560921, 2109659, 8004331, 30762570, 119322599, 466458505, 1840186572, 7303994132, 29192626506, 117376023897, 474341080495, 1927412337418, 7865914630990, 32242731996163, 132707758649954, 548168330676156, 2272568359911595

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, 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: A219232 A073193 A148151 * A148153 A148154 A148155

Adjacent sequences: A148149 A148150 A148151 * A148153 A148154 A148155

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved