A151247 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, 0), (1, 0, 0), (1, 1, 1)}

1, 4, 17, 75, 345, 1618, 7703, 36998, 179083, 871140, 4256643, 20864175, 102558243, 505175772, 2493153945, 12322236807, 60984538737, 302142060934, 1498421712545, 7437079389365, 36939846335989, 183591483762768, 912975651895035, 4542266727736862, 22608986355743263, 112578012850450138

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, -1 + j, 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: A346740 A265680 A255714 * A290914 A117439 A081910

Adjacent sequences: A151244 A151245 A151246 * A151248 A151249 A151250

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved