A148778 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, 1, -1), (1, 0, 1)}.

1, 1, 3, 8, 23, 75, 242, 797, 2722, 9358, 32361, 113558, 401386, 1423419, 5080996, 18236262, 65633113, 237023257, 859125261, 3121571670, 11366570789, 41490482518, 151752532780, 555940056833, 2040133494268, 7498551097214, 27597459751318, 101697901462645, 375227305219404, 1385969645879384

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[i, -1 + 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: A134758 A050511 A151405 * A099265 A099266 A024716

Adjacent sequences: A148775 A148776 A148777 * A148779 A148780 A148781

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved