A149744 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, 0), (1, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 79, 299, 1435, 6015, 28977, 127111, 615779, 2781585, 13528281, 62333163, 304059931, 1420849033, 6947386979, 32805454397, 160719098405, 765023055849, 3754056222261, 17982361242179, 88362997996283, 425418683915779, 2092924334272323, 10118080587391413, 49828855224311489, 241722588853373269

Offset

0,3

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A293458 A009234 A211474 * A149745 A149746 A149747

Adjacent sequences: A149741 A149742 A149743 * A149745 A149746 A149747

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved