A149092 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), (0, 0, 1), (0, 1, -1), (1, 0, -1), (1, 1, -1)}.

1, 1, 4, 8, 31, 87, 323, 1081, 3973, 14445, 54212, 204544, 786923, 3038695, 11904138, 46856916, 185950943, 742818757, 2981832628, 12038056472, 48820715319, 198765075087, 812772546171, 3334144388475, 13723690769043, 56666703823593, 234592663532672, 973902799859392, 4052797675504189

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + 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: A080072 A374319 A149091 * A188117 A094502 A162459

Adjacent sequences: A149089 A149090 A149091 * A149093 A149094 A149095

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved