A150120 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), (1, 1, 1)}.

1, 2, 6, 20, 68, 238, 854, 3106, 11410, 42306, 158018, 593584, 2240768, 8495266, 32324970, 123387316, 472303236, 1812388378, 6970142194, 26859338508, 103688368988, 400934226330, 1552607935314, 6020629027306, 23375746862394, 90863668091710, 353572653080462, 1377200901358688, 5369281685900048

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[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: A127152 A279557 A363182 * A360219 A360294 A150121

Adjacent sequences: A150117 A150118 A150119 * A150121 A150122 A150123

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved