A148963 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), (0, 1, 1), (1, 0, -1), (1, 1, -1)}.

1, 1, 3, 9, 31, 104, 408, 1538, 6182, 25115, 103973, 437297, 1865584, 8026201, 34960157, 153287512, 677730838, 3016052369, 13500654582, 60768654839, 274855397216, 1248660513549, 5696218856322, 26080901552357, 119831082369070, 552327548745745, 2553293503566385, 11835941043404728, 55006229868240849

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[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: A027092 A148961 A148962 * A027031 A027094 A027033

Adjacent sequences: A148960 A148961 A148962 * A148964 A148965 A148966

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved