A149171 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), (0, -1, 0), (0, 0, -1), (1, 1, 0)}.

1, 1, 4, 10, 33, 115, 391, 1439, 5405, 20303, 79050, 311520, 1230961, 4964657, 20189652, 82314358, 340130593, 1413947795, 5890309480, 24773921096, 104674234969, 443030309859, 1888676636461, 8080601115239, 34621402879031, 149177215251621, 644645021479230, 2789004825787100, 12121746816861675

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[i, j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A122948 A317800 A357799 * A149172 A338296 A105680

Adjacent sequences: A149168 A149169 A149170 * A149172 A149173 A149174

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved