A148636 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, -1, 1), (1, 0, -1), (1, 0, 1)}.

1, 1, 3, 6, 22, 61, 221, 715, 2677, 9456, 36176, 134565, 526917, 2028208, 8091308, 31929777, 129378035, 520401679, 2135953773, 8722585918, 36193244102, 149624642757, 626656142107, 2617098759731, 11049094963395, 46543855094639, 197872752185473, 839747689320864, 3591806175639896

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, 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] + 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: A148634 A323924 A148635 * A148637 A148638 A148639

Adjacent sequences: A148633 A148634 A148635 * A148637 A148638 A148639

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved