A148206 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), (0, 1, 0), (1, 1, -1)}.

1, 1, 2, 4, 12, 35, 123, 421, 1576, 5891, 23087, 91259, 370459, 1519776, 6337233, 26681825, 113581304, 487443036, 2108776238, 9183762845, 40244481167, 177314468256, 785126740297, 3491955994631, 15594314705119, 69899003379185, 314376552573569, 1418342696862853, 6417386874955452

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, 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: A151525 A148205 A019447 * A148207 A331621 A334250

Adjacent sequences: A148203 A148204 A148205 * A148207 A148208 A148209

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved