A150126 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, 1, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 6, 20, 70, 258, 964, 3650, 13988, 53912, 209250, 815694, 3191352, 12528050, 49293582, 194381732, 767871008, 3037741072, 12033319364, 47718165076, 189406078340, 752422637326, 2991131523890, 11898248359866, 47355226692644, 188565712004266, 751180820543044, 2993580743243248

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[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: A372526 A092413 A151285 * A150127 A151286 A047126

Adjacent sequences: A150123 A150124 A150125 * A150127 A150128 A150129

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved