A150202 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, 0, 1), (1, -1, -1), (1, 1, 0)}.

1, 2, 6, 21, 80, 311, 1270, 5312, 22519, 96946, 422507, 1855251, 8209543, 36577480, 163796018, 736910489, 3329734404, 15098891288, 68685017199, 313380803066, 1433548255821, 6573060361503, 30204501852140, 139070528970440, 641476436597421, 2963853258368986, 13715373177290459, 63559580855588337

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, 1 + j, 1 + k, -1 + n] + aux[i, 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: A150199 A150200 A150201 * A374554 A106223 A196345

Adjacent sequences: A150199 A150200 A150201 * A150203 A150204 A150205

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved