A148635 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, -1), (0, 0, -1), (1, -1, 1), (1, 0, 1)}.

1, 1, 3, 6, 22, 61, 221, 715, 2631, 9410, 35256, 133053, 509705, 1985164, 7789874, 30950573, 124019573, 500123818, 2037158956, 8323345250, 34325148556, 141934974210, 590948181102, 2469466634992, 10364625848330, 43695896253794, 184742552014020, 784488681432788, 3339338822434850

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A148633 A148634 A323924 * A148636 A148637 A148638

Adjacent sequences: A148632 A148633 A148634 * A148636 A148637 A148638

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved