A148060 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), (-1, -1, 1), (-1, 1, -1), (1, 0, 1)}.

1, 1, 2, 3, 12, 25, 77, 161, 676, 1629, 5631, 13233, 56856, 146445, 534726, 1335663, 5817552, 15578341, 58752167, 152411825, 669911668, 1840568181, 7092254088, 18880772519, 83533908814, 233748333865, 914652294617, 2481366615201, 11032801951506, 31299828328161, 123901443023541, 341011261634337

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[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A084728 A099429 A049601 * A148061 A148062 A148063

Adjacent sequences: A148057 A148058 A148059 * A148061 A148062 A148063

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved