A148081 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, -1), (0, -1, 1), (0, 1, 0), (1, 0, -1)}.

1, 1, 2, 4, 9, 24, 65, 192, 580, 1769, 5600, 18261, 60327, 204364, 695916, 2390408, 8372916, 29567259, 105555351, 380076126, 1372150571, 4999652704, 18372034289, 67871175118, 252393439474, 941509545219, 3525458643396, 13285908529457, 50291134312222, 191155727584836, 729023307273060, 2786384917159514

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A093156 A148079 A148080 * A148082 A148083 A200966

Adjacent sequences: A148078 A148079 A148080 * A148082 A148083 A148084

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved