A150329 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), (0, 1, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 22, 87, 327, 1364, 5609, 24137, 104261, 459753, 2043417, 9186095, 41589648, 189744503, 870532638, 4016599027, 18615600044, 86650307518, 404816959986, 1897682845381, 8922963170347, 42072570603419, 198878710231577, 942293136148628, 4474141653513842, 21285837229219130, 101452617756633714

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + 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: A150326 A150327 A150328 * A323681 A150330 A150331

Adjacent sequences: A150326 A150327 A150328 * A150330 A150331 A150332

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved