A150881 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, 1), (0, 1, -1), (0, 1, 1), (1, -1, 1), (1, 1, 0)}.

1, 2, 8, 33, 148, 681, 3207, 15307, 73822, 358559, 1751143, 8587649, 42250473, 208397918, 1030017125, 5099350476, 25279913728, 125465667926, 623278510259, 3098721059515, 15416066743763, 76738380083743, 382176833557163, 1904142981324656, 9490603393188092, 47318029786249952, 235982999815553655

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150878 A150879 A150880 * A053817 A150882 A150883

Adjacent sequences: A150878 A150879 A150880 * A150882 A150883 A150884

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved