A148481 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), (-1, 0, 1), (0, 0, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 2, 6, 20, 73, 272, 1040, 4177, 17264, 72861, 311631, 1349356, 5922851, 26295985, 117817978, 531665582, 2415053676, 11040435677, 50762362640, 234552661491, 1088404398909, 5070457777960, 23708810322816, 111236246629822, 523484373005358, 2470328346542832, 11687294570928665, 55425802377348044

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A195186 A150137 A150138 * A150139 A052884 A150140

Adjacent sequences: A148478 A148479 A148480 * A148482 A148483 A148484

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved