A149217 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, 1), (-1, 1, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 10, 42, 136, 598, 2162, 9815, 37636, 174615, 694695, 3271551, 13352629, 63547908, 264327829, 1267696988, 5350969987, 25811875559, 110238766866, 534157611947, 2303345758002, 11200561768291, 48687212201572, 237436053622265, 1039149699997593, 5079720276433999, 22362113435873612

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A149214 A149215 A149216 * A149218 A149219 A361938

Adjacent sequences: A149214 A149215 A149216 * A149218 A149219 A149220

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved