A150459 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, 0), (1, 1, -1), (1, 1, 1)}.

1, 2, 7, 25, 97, 388, 1603, 6740, 28805, 124516, 543663, 2392639, 10602985, 47261506, 211741279, 952868309, 4304985813, 19517751988, 88766948783, 404856105533, 1851243940981, 8484777279218, 38971298126171, 179349906574808, 826880449091957, 3818656084434754, 17662498926983907, 81812675829911287

Offset

0,2

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, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, 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: A355628 A276903 A150458 * A150460 A150461 A150462

Adjacent sequences: A150456 A150457 A150458 * A150460 A150461 A150462

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved