A149089 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, 0), (-1, -1, 1), (-1, 0, 1), (1, 1, 0)}.

1, 1, 4, 7, 32, 68, 320, 747, 3588, 8884, 43112, 111054, 542840, 1439280, 7068896, 19157363, 94420380, 260343268, 1286463464, 3596962122, 17809428792, 50372422384, 249792782560, 713390782142, 3542022471496, 10199612069128, 50692207741840, 147016742815612, 731273455228208, 2134040173232352

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A000289 A241426 A271676 * A004031 A243863 A153062

Adjacent sequences: A149086 A149087 A149088 * A149090 A149091 A149092

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved