A148082 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), (1, -1, -1), (1, 0, 0)}.

1, 1, 2, 4, 9, 24, 65, 197, 590, 1831, 5907, 19246, 65628, 223075, 772202, 2715962, 9613099, 34850427, 126250204, 462501869, 1709044861, 6342910025, 23890157291, 89977511284, 341462174862, 1302976354195, 4987822604239, 19285789090167, 74581371919137, 290008960011264, 1132019544597872, 4429381684162681

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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] + 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: A148079 A148080 A148081 * A148083 A200966 A148084

Adjacent sequences: A148079 A148080 A148081 * A148083 A148084 A148085

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved