A148581 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, 0, -1), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 6, 20, 52, 180, 531, 1935, 6087, 23075, 76002, 294690, 1007573, 3967709, 13952603, 55705977, 200096396, 808097516, 2954315100, 12036963816, 44673868259, 183352067367, 689141233096, 2846666932970, 10814730959009, 44922309300087, 172272809441244, 719005305749812, 2780261740311903

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, -1 + j, 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, 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: A148579 A151263 A148580 * A148582 A148583 A148584

Adjacent sequences: A148578 A148579 A148580 * A148582 A148583 A148584

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved