A150998 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), (1, 1, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 38, 173, 811, 3849, 18466, 89607, 436576, 2136997, 10505680, 51760229, 255580298, 1264625226, 6265229147, 31076772966, 154320198127, 766900717629, 3813872974918, 18979320285386, 94494410482769, 470682057046603, 2345467942988451, 11691550126914933, 58296753148994862, 290760597805640268

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, -1 + j, k, -1 + n] + aux[-1 + i, -1 + 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: A150995 A150996 A150997 * A150999 A151000 A151001

Adjacent sequences: A150995 A150996 A150997 * A150999 A151000 A151001

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved