A148416 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, -1), (1, -1, 1), (1, 0, 0)}.

1, 1, 2, 5, 17, 61, 234, 935, 3834, 16099, 68800, 298743, 1314381, 5847047, 26259408, 118899489, 542185061, 2487712901, 11476655590, 53200947263, 247676625637, 1157496494273, 5428210480192, 25536009034995, 120471803123458, 569830600657011, 2701712842966650, 12837554523138593, 61122512592654635

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A360211 A112832 A148415 * A259792 A003456 A109084

Adjacent sequences: A148413 A148414 A148415 * A148417 A148418 A148419

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved