A149148 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), (-1, -1, 1), (-1, 0, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 9, 38, 111, 487, 1613, 7266, 25898, 118756, 444424, 2062730, 7995233, 37424774, 148969816, 701627984, 2851691801, 13493743151, 55771863728, 264858505725, 1109897493977, 5286000156990, 22407811546785, 106967054294187, 457894679334773, 2189983001429080, 9453661460869249, 45285465488383829

Offset

0,3

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A289157 A149146 A149147 * A149149 A149150 A149151

Adjacent sequences: A149145 A149146 A149147 * A149149 A149150 A149151

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved