A149875 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, 0), (-1, -1, 1), (-1, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 5, 13, 45, 150, 548, 1895, 7595, 28565, 115446, 438694, 1862878, 7407410, 31401854, 125165643, 548208863, 2251065516, 9811745632, 40261665482, 179765822208, 753826837023, 3345833966405, 14001164979883, 63337842696640, 269572598312974, 1211822937294886, 5143408328423039

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A212828 A212830 A000719 * A221546 A085632 A378584

Adjacent sequences: A149872 A149873 A149874 * A149876 A149877 A149878

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved