A148088 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), (-1, 1, 1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 4, 10, 24, 68, 191, 571, 1723, 5293, 16671, 53094, 172307, 563812, 1861398, 6205635, 20824194, 70511559, 240014778, 821599856, 2827041912, 9769219609, 33929479056, 118266254690, 413775330014, 1452493361222, 5113896832373, 18062859626325, 63964741855443, 227106603716388, 808239933828179

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A121186 A309505 A309504 * A028506 A029893 A148089

Adjacent sequences: A148085 A148086 A148087 * A148089 A148090 A148091

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved