A150996 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, 0), (0, 1, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 38, 172, 794, 3738, 17830, 85774, 415198, 2020718, 9873217, 48400818, 237896624, 1171802761, 5782520122, 28578832172, 141428488154, 700672333743, 3474632854006, 17245086671574, 85652143372137, 425684645188303, 2116810581506954, 10531537984565389, 52419539328903339, 261014994119075193

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, 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: A150993 A150994 A150995 * A150997 A150998 A150999

Adjacent sequences: A150993 A150994 A150995 * A150997 A150998 A150999

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved