A148989 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, 3, 9, 33, 114, 444, 1699, 6929, 27913, 117303, 489207, 2099583, 8964785, 39080063, 169775056, 749045576, 3297109440, 14686154108, 65314573848, 293187891314, 1314756153955, 5939658404153, 26816936739619, 121804055191199, 553053297199063, 2523534497780651, 11513095822773133, 52741015760769921

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, -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: A192430 A323790 A148988 * A047117 A148990 A184512

Adjacent sequences: A148986 A148987 A148988 * A148990 A148991 A148992

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved