A148239 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), (-1, 1, 1), (0, 0, -1), (1, 0, 0)}.

1, 1, 2, 4, 13, 36, 110, 335, 1104, 3753, 13113, 44896, 157137, 567676, 2089014, 7618757, 28048073, 104358663, 393485284, 1490450576, 5677409041, 21612120855, 83008243421, 321100456265, 1248397782434, 4848574226724, 18933502431439, 74199883431670, 292243868198435, 1152756680020786, 4562800834642942

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, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + 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: A148237 A148238 A278281 * A148240 A151354 A148241

Adjacent sequences: A148236 A148237 A148238 * A148240 A148241 A148242

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved