A148759 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, 1), (0, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 7, 29, 78, 338, 1058, 4686, 15803, 71729, 253562, 1169404, 4288926, 19974730, 75412117, 353859401, 1366111116, 6451741800, 25355370298, 120372620960, 480181343782, 2289045790648, 9247921966268, 44237902037162, 180665568976249, 866824352303161, 3573205164846309, 17188580145141317

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, -1 + 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: A080806 A321191 A363666 * A148760 A148761 A186732

Adjacent sequences: A148756 A148757 A148758 * A148760 A148761 A148762

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved