A151228 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), (0, 1, 1), (1, 0, 1), (1, 1, 1)}.

1, 3, 13, 58, 275, 1301, 6326, 30693, 150617, 739484, 3649152, 18021798, 89258150, 442338523, 2195951351, 10907181445, 54234272375, 269792089940, 1343053821128, 6688305795229, 33323800239239, 166081023119789, 828021461327650, 4129203071546505, 20597135139617907, 102761720156567122

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + 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: A151226 A151320 A151227 * A366676 A339881 A336791

Adjacent sequences: A151225 A151226 A151227 * A151229 A151230 A151231

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved