A148076 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, -1, 1), (-1, 1, 0), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 4, 9, 21, 61, 174, 529, 1641, 5095, 16033, 53457, 179040, 611600, 2114005, 7286191, 25434141, 90624740, 324820786, 1175997883, 4277780903, 15565099278, 57172451188, 211915699815, 789384452140, 2957220530771, 11099880354961, 41758569166532, 158093763382620, 601507196523586, 2297362832884187

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + 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: A148075 A351364 A058718 * A217976 A156801 A363771

Adjacent sequences: A148073 A148074 A148075 * A148077 A148078 A148079

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved