A148739 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, 0, 0), (-1, 1, 1), (0, -1, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 7, 25, 86, 342, 1382, 5856, 25260, 111301, 497087, 2247763, 10267545, 47299472, 219526072, 1025314405, 4815497410, 22726304664, 107713530687, 512449081616, 2446184163135, 11711950445834, 56225920974939, 270579932260223, 1304982830765365, 6306323693669719, 30530398362465194

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, j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148736 A148737 A148738 * A129084 A287892 A343278

Adjacent sequences: A148736 A148737 A148738 * A148740 A148741 A148742

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved