A148583 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), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 6, 20, 54, 167, 528, 1672, 5471, 17981, 60139, 203024, 687400, 2361146, 8129436, 28138474, 98079577, 342877988, 1203994543, 4242357232, 14998885029, 53192103457, 189077433312, 674049702154, 2408310185281, 8621409878132, 30930738955158, 111168756778109, 400226995774209, 1443243712653720

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[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: A148580 A148581 A148582 * A148584 A148585 A148586

Adjacent sequences: A148580 A148581 A148582 * A148584 A148585 A148586

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved