A150035 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), (-1, -1, 0), (0, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 2, 6, 17, 62, 220, 841, 3189, 12794, 51277, 209888, 865350, 3629443, 15285646, 64947866, 277884512, 1197339560, 5179481837, 22524304974, 98421284540, 431715987739, 1899744576945, 8390256984160, 37173779175025, 165129807238379, 735393899723485, 3283605964246124, 14694311017578848

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A000687 A085827 A347825 * A000661 A150036 A150037

Adjacent sequences: A150032 A150033 A150034 * A150036 A150037 A150038

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved