A149416 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, 0), (-1, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 54, 184, 868, 3270, 15797, 62573, 306060, 1252011, 6168402, 25808068, 127724851, 543318743, 2696792155, 11618463835, 57783118598, 251466517576, 1252361879418, 5495032545579, 27393340026109, 121016104496380, 603706939462674, 2682399778543295, 13388555204024655, 59782410913675045

Offset

0,3

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149414 A053454 A149415 * A149417 A151478 A125528

Adjacent sequences: A149413 A149414 A149415 * A149417 A149418 A149419

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved