A151131 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, 0), (0, 0, -1), (0, 1, 0), (0, 1, 1), (1, 0, 1)}

1, 3, 11, 45, 198, 882, 4006, 18505, 86473, 406981, 1928110, 9185789, 43958967, 211147220, 1017380648, 4915403582, 23804986783, 115526616241, 561669161351, 2735112582225, 13338235034978, 65130900798744, 318406433843562, 1558239000906143, 7633165587296164, 37424723726355602, 183638260399843749

Offset

0,2

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A217890 A001003 A080243 * A151132 A200075 A187764

Adjacent sequences: A151128 A151129 A151130 * A151132 A151133 A151134

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved