A148374 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, -1), (-1, -1, 1), (-1, 0, 1), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 5, 16, 43, 149, 461, 1660, 5517, 20589, 71521, 273554, 982725, 3825252, 14100377, 55646674, 209278507, 835163345, 3192074879, 12855707644, 49794667899, 202085622420, 791540599641, 3233410039356, 12785696597115, 52523977727955, 209398814952955, 864450841225340, 3470957953117151

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[i, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A148372 A148373 A132734 * A182884 A152428 A317890

Adjacent sequences: A148371 A148372 A148373 * A148375 A148376 A148377

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved