A150147 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, -1), (1, 0, 0)}.

1, 2, 6, 20, 73, 286, 1171, 4930, 21176, 92591, 411017, 1846504, 8372732, 38262960, 176083803, 815325551, 3795021644, 17743531775, 83289442421, 392377483784, 1854492950529, 8790179694611, 41772641587849, 198979876476148, 949875548782681, 4543447373982078, 21771657538903904, 104501228825358146

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, j, k, -1 + n] + aux[-1 + i, j, 1 + 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: A243255 A150145 A150146 * A150148 A150149 A150150

Adjacent sequences: A150144 A150145 A150146 * A150148 A150149 A150150

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved