A148899 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, 1), (0, 1, -1), (0, 1, 1), (1, -1, 1)}.

1, 1, 3, 8, 31, 107, 407, 1563, 6307, 25314, 104211, 434811, 1834609, 7775478, 33349109, 144050282, 625106289, 2726906876, 11972170104, 52763988723, 233310974520, 1035974027077, 4617039746546, 20628654645010, 92422614238745, 415320306918677, 1870678443468084, 8442702168395044, 38189122706303356

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A151534 A148897 A148898 * A148900 A148901 A148902

Adjacent sequences: A148896 A148897 A148898 * A148900 A148901 A148902

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved