A148897 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, 1, -1), (0, 1, 1), (1, -1, 1)}.

1, 1, 3, 8, 31, 107, 402, 1553, 6212, 24929, 102365, 425855, 1796311, 7595044, 32541726, 140436897, 608624581, 2653313910, 11639255932, 51259909476, 226553582890, 1005350577805, 4478742370310, 20003242199184, 89586533301990, 402467873379907, 1812302250341527, 8177362568979110, 36982173683781310

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, 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: A148895 A148896 A151534 * A148898 A148899 A148900

Adjacent sequences: A148894 A148895 A148896 * A148898 A148899 A148900

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved