A148960 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, 0, 0), (1, -1, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 31, 100, 375, 1377, 5342, 20385, 81729, 324695, 1327214, 5392983, 22420498, 92871577, 391003924, 1642607275, 6989242210, 29703203101, 127498712366, 546985579534, 2365391951308, 10228061429132, 44514902639093, 193783765825669, 848094078035421, 3713313737751062, 16331191377025653

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, 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: A138281 A049416 A148959 * A027029 A027092 A148961

Adjacent sequences: A148957 A148958 A148959 * A148961 A148962 A148963

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved