A150380 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, 0), (-1, 1, 1), (1, 0, 0), (1, 1, -1), (1, 1, 0)}.

1, 2, 7, 23, 96, 370, 1649, 6853, 31452, 136477, 637326, 2844663, 13440854, 61193764, 291569929, 1346960293, 6458143571, 30168044434, 145347894835, 684914837573, 3312708466632, 15719981712073, 76273840443727, 364024533938763, 1770924934795926, 8492183008718931, 41405426740818565, 199348382095843560

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[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A150377 A150378 A150379 * A150381 A150382 A150383

Adjacent sequences: A150377 A150378 A150379 * A150381 A150382 A150383

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved