A150472 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, 0, 0), (0, -1, 1), (0, 1, 0), (0, 1, 1), (1, 0, -1)}.

1, 2, 7, 25, 99, 403, 1719, 7451, 33116, 148742, 678430, 3117059, 14468349, 67515160, 317323787, 1497442597, 7103751478, 33805337279, 161517974750, 773643738505, 3717199351855, 17896679846060, 86379015071009, 417611710091614, 2023077824973609, 9814381630455424, 47690808627818067, 232019200929515380

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150469 A150470 A150471 * A150473 A150474 A150475

Adjacent sequences: A150469 A150470 A150471 * A150473 A150474 A150475

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved