A148992 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, 0), (-1, 0, 0), (0, -1, 1), (0, 1, 1), (1, 1, -1)}.

1, 1, 3, 9, 33, 116, 453, 1750, 7109, 28986, 121305, 510680, 2183305, 9395165, 40817884, 178419362, 785115490, 3472402376, 15435999223, 68908079136, 308841287833, 1389102439531, 6268241975771, 28368390147122, 128738944006402, 585688702070794, 2670712676908657, 12204424325272461, 55881736244853004

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 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: A148990 A184512 A148991 * A148993 A148994 A148995

Adjacent sequences: A148989 A148990 A148991 * A148993 A148994 A148995

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved