A148078 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, -1, 0), (-1, 0, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 4, 9, 24, 60, 187, 533, 1633, 5160, 15870, 53517, 171668, 585244, 1975988, 6674839, 23482783, 80233596, 286909515, 1007392268, 3586586050, 12951852657, 46106951430, 169300422921, 610788829219, 2244880160948, 8256288325005, 30256079492301, 112973372869465, 416123464655364, 1560839118401024

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[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A038664 A261367 A148077 * A093156 A148079 A148080

Adjacent sequences: A148075 A148076 A148077 * A148079 A148080 A148081

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved