A150333 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), (1, -1, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 22, 89, 337, 1436, 5842, 25590, 108678, 484318, 2110606, 9514734, 42201925, 191847029, 861588143, 3941534667, 17866347492, 82141080518, 374987229911, 1730954651365, 7946514248752, 36803589555453, 169724804310792, 788272889426298, 3648777374217957, 16987200920762030, 78875741939670272

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[-1 + 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: A150330 A150331 A150332 * A057787 A217138 A004300

Adjacent sequences: A150330 A150331 A150332 * A150334 A150335 A150336

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved