A150145 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, 0), (0, 0, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 20, 73, 285, 1148, 4779, 20334, 88008, 386678, 1718210, 7712724, 34911184, 159158001, 730223827, 3368483512, 15614541300, 72693167654, 339721530052, 1593166776075, 7494694158385, 35357515510128, 167237574738609, 792892967407281, 3767403585314309, 17936611598970073, 85554869014994671

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, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150143 A150144 A243255 * A150146 A150147 A150148

Adjacent sequences: A150142 A150143 A150144 * A150146 A150147 A150148

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved