A148347 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), (-1, 1, -1), (0, 1, 1), (1, -1, 0)}

1, 1, 2, 5, 15, 39, 127, 405, 1330, 4478, 15616, 54421, 194793, 702460, 2566274, 9451947, 35193820, 131845947, 497775471, 1891195411, 7227861089, 27762928862, 107200840091, 415720406354, 1619020483150, 6329515027431, 24836077599153, 97777922664752, 386164569404667, 1529668930872126, 6076165429767563

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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

Crossrefs

Sequence in context: A148344 A148345 A148346 * A309299 A151260 A148348

Adjacent sequences: A148344 A148345 A148346 * A148348 A148349 A148350

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved