A150919 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, 1, -1), (1, -1, 1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 32, 153, 635, 3096, 13728, 67538, 310247, 1533967, 7199858, 35708102, 170003438, 844851977, 4062567880, 20217757280, 97929440507, 487846650396, 2375996475404, 11845115755542, 57935345799137, 288989257917447, 1418207449022448, 7077278886801328, 34825043435962323, 173846410464724864

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -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, 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: A150916 A150917 A150918 * A150920 A013501 A179230

Adjacent sequences: A150916 A150917 A150918 * A150920 A150921 A150922

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved