A150306 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, 0, 0), (-1, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 21, 83, 287, 1211, 4518, 19806, 77422, 347954, 1403992, 6420476, 26507997, 122781595, 515819832, 2412709928, 10275378478, 48434841254, 208558848383, 989231211470, 4298367330512, 20492961935275, 89724014122893, 429614370348584, 1893163878581018, 9097972278059646, 40315324000448876

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150303 A150304 A150305 * A150307 A321283 A150308

Adjacent sequences: A150303 A150304 A150305 * A150307 A150308 A150309

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved