A149889 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, 0), (1, 0, 1)}.

1, 2, 5, 14, 45, 153, 548, 2019, 7605, 29388, 115571, 460172, 1860049, 7599867, 31298912, 130183426, 545493796, 2298658623, 9754411712, 41617449285, 178315326510, 768003319937, 3321490251318, 14412632043743, 62791261002627, 274457598076597, 1202860829073499, 5288629250797523

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[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: A240610 A149887 A149888 * A149890 A149891 A149892

Adjacent sequences: A149886 A149887 A149888 * A149890 A149891 A149892

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved