A150936 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, 1), (1, -1, 1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 33, 161, 680, 3369, 15088, 75081, 347064, 1730781, 8158649, 40732877, 194526790, 971772573, 4683554583, 23404834485, 113561913832, 567609536625, 2768123587989, 13837451513575, 67749630403142, 338696889044933, 1663493549344340, 8316622638737221, 40949858508495618, 204735162202289217

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + 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: A150933 A150934 A150935 * A109719 A263685 A334443

Adjacent sequences: A150933 A150934 A150935 * A150937 A150938 A150939

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved