A150168 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, 1), (0, 1, 0), (1, 0, -1), (1, 1, 0)}.

1, 2, 6, 20, 75, 297, 1223, 5178, 22441, 98884, 442283, 2000916, 9142251, 42116199, 195395624, 912044028, 4279777216, 20176137436, 95507078481, 453744740526, 2162709310394, 10338309423180, 49549707152860, 238047836414608, 1146105257197884, 5528901726159039, 26719869652877299, 129343971140839144

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, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A148483 A150166 A150167 * A145870 A134957 A052889

Adjacent sequences: A150165 A150166 A150167 * A150169 A150170 A150171

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved