A150056 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, 1, 0), (1, 1, 0)}.

1, 2, 6, 18, 62, 220, 816, 3066, 11770, 45840, 181100, 722238, 2904590, 11764740, 47972960, 196737634, 810804722, 3355892888, 13944611892, 58151327382, 243285478982, 1020779890348, 4294333356808, 18109979756186, 76545364440266, 324206304160480, 1375801674684476, 5848739616028206

Offset

0,2

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, k, -1 + n] + aux[i, -1 + j, 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: A150054 A067052 A150055 * A204686 A098964 A079469

Adjacent sequences: A150053 A150054 A150055 * A150057 A150058 A150059

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved