A149349 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, 0, 0), (0, 0, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 42, 153, 595, 2343, 9542, 39413, 166281, 708897, 3061940, 13353865, 58750955, 260487890, 1162823080, 5222031742, 23582500740, 107010241453, 487788886128, 2232519065432, 10255861643899, 47276532426065, 218615273009775, 1013881795097680, 4714877471655987, 21980833198519547

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A149347 A173411 A149348 * A149350 A149351 A149352

Adjacent sequences: A149346 A149347 A149348 * A149350 A149351 A149352

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved