A151103 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), (0, 0, 1), (0, 1, -1), (0, 1, 1), (1, 0, 0)}.

1, 3, 11, 43, 183, 805, 3623, 16590, 76954, 360408, 1700669, 8075427, 38538364, 184683663, 888178746, 4284291845, 20719508879, 100427985517, 487736356011, 2372840838486, 11561668390609, 56411788626048, 275585068169835, 1347800508677689, 6598339039455263, 32332818429735453, 158568949209761361

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A063031 A151101 A151102 * A049189 A049163 A049180

Adjacent sequences: A151100 A151101 A151102 * A151104 A151105 A151106

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved