A150868 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, 0, 0), (0, -1, 1), (0, 0, 1), (0, 1, -1), (1, 1, 1)}.

1, 2, 8, 33, 145, 651, 2985, 13880, 65145, 308299, 1467469, 7019724, 33714258, 162456912, 785064404, 3802866986, 18459984428, 89772495880, 437275226693, 2132984726293, 10417766696602, 50940183448809, 249342704115073, 1221636782170665, 5990468787616224, 29398246699893197, 144376495827307323

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150866 A150867 A255951 * A150869 A150870 A150871

Adjacent sequences: A150865 A150866 A150867 * A150869 A150870 A150871

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved