A150893 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, 1), (0, 1, 0), (1, -1, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 8, 34, 154, 718, 3410, 16382, 79390, 387116, 1896476, 9324092, 45970110, 227144536, 1124339206, 5573348284, 27659659494, 137404653624, 683140842472, 3398734743336, 16919095260322, 84266075811002, 419868825524958, 2092832028965694, 10435032990758858, 52044422407700982, 259633319793721384

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A074606 A002928 A150892 * A235038 A150894 A150895

Adjacent sequences: A150890 A150891 A150892 * A150894 A150895 A150896

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved