A148105 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, 1), (0, 1, -1), (1, -1, 1), (1, 0, 0)}.

1, 1, 2, 4, 10, 27, 79, 242, 770, 2526, 8482, 29081, 101381, 358448, 1282833, 4638642, 16923338, 62222809, 230338989, 857789608, 3211367100, 12079381400, 45627168971, 172996707877, 658150503220, 2511554427265, 9610919774235, 36870810085355, 141774779218300, 546295776440781, 2109079351378737

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A157003 A245900 A114507 * A127386 A279551 A148106

Adjacent sequences: A148102 A148103 A148104 * A148106 A148107 A148108

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved