A148571 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), (-1, 0, 1), (0, 1, -1), (1, -1, 0), (1, 0, 0)}.

1, 1, 3, 6, 19, 53, 174, 578, 1995, 7216, 26344, 99728, 381800, 1492177, 5915918, 23744011, 96564899, 396388960, 1644245678, 6876168960, 28989823670, 123106176598, 526195843753, 2263275385587, 9788573310743, 42562654829075, 185963233778672, 816227682031374, 3597876689102063

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148569 A024998 A148570 * A345400 A148572 A320174

Adjacent sequences: A148568 A148569 A148570 * A148572 A148573 A148574

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved