A149728 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, 0, 1), (0, 1, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 75, 289, 1321, 5603, 26151, 115545, 546467, 2476781, 11824411, 54562395, 262245791, 1225932563, 5921776307, 27954464511, 135555532109, 644771630961, 3136297717081, 15007918416499, 73187078083773, 351930016225887, 1719847828600187, 8303424758407139, 40650829603059627, 196922384481104843

Offset

0,3

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, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A149725 A149726 A149727 * A149729 A282963 A149730

Adjacent sequences: A149725 A149726 A149727 * A149729 A149730 A149731

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved