A148821 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), (-1, 1, 0), (0, 0, -1), (1, -1, 1), (1, 0, 1)}.

1, 1, 3, 8, 26, 92, 327, 1193, 4562, 17685, 69588, 279436, 1133916, 4641173, 19219142, 80216046, 336914408, 1425417925, 6066920841, 25945712001, 111518261524, 481520271363, 2087017917106, 9079448783803, 39640509733005, 173602219516008, 762503437509516, 3358590618438060, 14831233518450775

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A124383 A148819 A148820 * A074506 A215087 A148822

Adjacent sequences: A148818 A148819 A148820 * A148822 A148823 A148824

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved