A148355 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), (0, 0, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 5, 15, 45, 145, 479, 1673, 5928, 21602, 79826, 300161, 1144599, 4414282, 17226535, 67793778, 269250387, 1077231445, 4339818022, 17600218203, 71764342984, 294309638092, 1212500814029, 5019282722556, 20864139620821, 87068515194275, 364733443455242, 1532912464126412, 6464562544654232

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, k, -1 + n] + aux[i, j, 1 + 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: A364330 A151279 A149907 * A148356 A206302 A149908

Adjacent sequences: A148352 A148353 A148354 * A148356 A148357 A148358

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved