A148998 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, -1), (-1, 0, 1), (0, -1, 1), (1, 1, -1), (1, 1, 0)}

1, 1, 3, 9, 33, 127, 479, 1987, 8153, 34531, 149741, 647735, 2870859, 12757149, 57208157, 259286825, 1176744359, 5390834697, 24773267651, 114338291417, 530595471509, 2466705308701, 11521350667943, 53941366645455, 253217223758335, 1192447189901931, 5624336512312905, 26601547030729237

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, 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] + aux[1 + i, 1 + 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: A138178 A063027 A364211 * A049185 A049162 A049176

Adjacent sequences: A148995 A148996 A148997 * A148999 A149000 A149001

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved