A148045 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), (-1, -1, 1), (-1, 1, 0), (1, 0, 0)}.

1, 1, 2, 3, 10, 20, 58, 119, 446, 1044, 3448, 7986, 31689, 79898, 281279, 694389, 2846170, 7495572, 27436672, 70493078, 295037033, 799668270, 3004460457, 7933577956, 33692390947, 93207860220, 356841845618, 961310281239, 4126690311286, 11592618439035, 45016592572833, 123137553148637, 532997729810330

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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, 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, 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: A285981 A264038 A148044 * A148046 A148047 A148048

Adjacent sequences: A148042 A148043 A148044 * A148046 A148047 A148048

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved