A149094 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), (-1, 1, 0), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 8, 32, 84, 346, 1035, 4434, 14276, 63150, 213816, 965176, 3397665, 15525463, 56362226, 259816633, 966364827, 4488211510, 17021512470, 79566536014, 306669648097, 1441164065549, 5631486475726, 26580640449773, 105101670791449, 497927703722680, 1989118558545756, 9454227000026822

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A094867 A377001 A149093 * A086344 A209084 A254216

Adjacent sequences: A149091 A149092 A149093 * A149095 A149096 A149097

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved