A150124 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, 1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 6, 20, 69, 250, 924, 3468, 13194, 50602, 195481, 759303, 2961868, 11595975, 45528334, 179189562, 706689736, 2791766580, 11045040490, 43751719084, 173495907556, 688634340547, 2735513747087, 10874199425535, 43253925280236, 172143832114877, 685437577427508, 2730427779738255

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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[i, -1 + 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: A199248 A148478 A148479 * A045631 A275046 A229472

Adjacent sequences: A150121 A150122 A150123 * A150125 A150126 A150127

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved