A150821 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), (1, 0, -1), (1, 0, 0), (1, 1, 1)}

1, 2, 8, 31, 142, 610, 2910, 13214, 64024, 299038, 1463073, 6954791, 34222168, 164581676, 812984647, 3941658778, 19522912255, 95216834229, 472523074541, 2314843383725, 11504299257859, 56551676630587, 281361065042868, 1386811012437061, 6905723951484690, 34111105861427435, 169974107467594724

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[-1 + 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: A003175 A129427 A150820 * A150822 A150823 A150824

Adjacent sequences: A150818 A150819 A150820 * A150822 A150823 A150824

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved