A149835 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), (0, 0, -1), (0, 1, 0), (1, 0, 0), (1, 1, -1)}.

1, 2, 4, 10, 30, 96, 324, 1138, 4134, 15464, 59198, 230678, 913916, 3672582, 14940794, 61426632, 254982076, 1067415522, 4502824810, 19124778850, 81738521776, 351324672662, 1517933308038, 6589522925548, 28732010239624, 125785366412276, 552750320877912, 2437456478786392, 10783477702624244

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A149834 A273958 A362637 * A149836 A003289 A087161

Adjacent sequences: A149832 A149833 A149834 * A149836 A149837 A149838

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved