A148495 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, 0, 1), (-1, 1, 1), (0, 1, 0), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 6, 21, 83, 348, 1499, 6623, 29805, 136080, 628537, 2930993, 13772875, 65132877, 309654749, 1478735723, 7088395315, 34089167561, 164401035964, 794796779867, 3850714202599, 18691819399273, 90885695919131, 442583806441116, 2158167279743194, 10536761139563128, 51500580609300347

Offset

0,3

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A032347 A032346 A329055 * A150221 A058866 A063689

Adjacent sequences: A148492 A148493 A148494 * A148496 A148497 A148498

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved