A148871 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, 1), (1, -1, 0)}.

1, 1, 3, 8, 29, 95, 352, 1317, 5178, 20231, 81681, 334624, 1385975, 5778504, 24432650, 104130924, 445996034, 1923136631, 8353882501, 36444183670, 159607590184, 702556782360, 3105431408159, 13766270203412, 61226929138240, 273267155552114, 1222860642385854, 5485030439556647, 24667732138034939

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[i, -1 + j, -1 + 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: A148868 A148869 A148870 * A148872 A148873 A148874

Adjacent sequences: A148868 A148869 A148870 * A148872 A148873 A148874

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved