A149717 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, 0), (-1, 0, 0), (0, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 73, 283, 1213, 5317, 23579, 105117, 472819, 2155691, 9930367, 45862131, 212768211, 991602657, 4648095447, 21872951307, 103168498481, 487859966969, 2313605012309, 11003549013929, 52448952239013, 250417531589871, 1197678828320871, 5738625425104709, 27544353854609085, 132399289932521771

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A187823 A297625 A084777 * A149718 A149719 A149720

Adjacent sequences: A149714 A149715 A149716 * A149718 A149719 A149720

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved