A148903 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, 1), (-1, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 32, 101, 417, 1473, 6355, 23885, 104937, 411589, 1836969, 7422031, 33475041, 138309499, 629036675, 2644169269, 12104444055, 51586010082, 237407217744, 1023169675566, 4729538714868, 20573894111580, 95454351607666, 418509678131013, 1947864101618615, 8597770562922403, 40126065061606563

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, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A176304 A368208 A180385 * A148904 A218882 A148905

Adjacent sequences: A148900 A148901 A148902 * A148904 A148905 A148906

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved