A150817 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), (0, 0, -1), (1, 0, 0), (1, 1, 1)}

1, 2, 8, 31, 136, 595, 2708, 12422, 57944, 272047, 1287966, 6127908, 29305248, 140661334, 677464577, 3271799317, 15840128961, 76849014880, 373533453669, 1818569852770, 8866788087181, 43288177910845, 211584687310466, 1035288521940909, 5070597363843572, 24856524622025733, 121947612958567187

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, k, -1 + n] + aux[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: A150814 A150815 A150816 * A150818 A009567 A150819

Adjacent sequences: A150814 A150815 A150816 * A150818 A150819 A150820

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved