A149108 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, 0, 0), (-1, 0, 1), (1, -1, -1), (1, 1, 0)}.

1, 1, 4, 8, 35, 98, 431, 1361, 6203, 21117, 97367, 349863, 1628534, 6075216, 28476830, 109268287, 514736603, 2019723490, 9551131625, 38146488279, 180943166799, 733323214843, 3486859436279, 14304847475503, 68153275274225, 282505125588502, 1348167924533795, 5638208585217986, 26943787555922353

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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A197157 A324410 A218628 * A149109 A266676 A046056

Adjacent sequences: A149105 A149106 A149107 * A149109 A149110 A149111

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved