A150032 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), (-1, 1, 1), (1, 0, 0), (1, 0, 1)}.

1, 2, 6, 16, 64, 216, 856, 2976, 12832, 48448, 205888, 782464, 3480192, 13840256, 60745088, 241676800, 1093548544, 4483687424, 20050686976, 82059288576, 375415300096, 1570813652992, 7111318892544, 29671917535232, 136795784593408, 580782992326656, 2652281254117376, 11224180146405376

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A121753 A173994 A363587 * A373452 A283420 A121749

Adjacent sequences: A150029 A150030 A150031 * A150033 A150034 A150035

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved