A148563 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, 0), (0, 0, 1), (0, 1, -1), (1, 0, -1)}.

1, 1, 3, 6, 18, 51, 160, 527, 1746, 6002, 21021, 74747, 272067, 998210, 3705377, 13910337, 52594731, 200939729, 773026916, 2991205863, 11650429891, 45599715229, 179454235667, 709767636218, 2818244126100, 11235949376444, 44956809578890, 180500485622687, 727223612401830, 2938597126810225

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148561 A123891 A148562 * A148564 A148565 A112572

Adjacent sequences: A148560 A148561 A148562 * A148564 A148565 A148566

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved