A149809 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, 0, 1), (-1, 1, 1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 93, 401, 1983, 9091, 45161, 213119, 1061479, 5093533, 25406273, 123181471, 614950881, 3002237019, 14995780171, 73566098813, 367575895361, 1809635077057, 9043881071507, 44643165355527, 223142191408821, 1103760893289289, 5517524581440889, 27336461138993745, 136659805451964033

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149807 A149808 A371836 * A263245 A346199 A020050

Adjacent sequences: A149806 A149807 A149808 * A149810 A149811 A149812

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved