A150421 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), (0, 0, 1), (1, 0, -1), (1, 0, 1)}.

1, 2, 7, 24, 95, 381, 1620, 6952, 30527, 135709, 611338, 2780105, 12737432, 58751582, 272577928, 1271185910, 5954217923, 27994989600, 132078328817, 625071178375, 2966491655428, 14113589173293, 67299639843727, 321581250955477, 1539569388429159, 7383627382685730, 35468227398650854, 170630590833547054

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + 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: A150418 A150419 A150420 * A150422 A137952 A005754

Adjacent sequences: A150418 A150419 A150420 * A150422 A150423 A150424

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved