A149003 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, 1), (0, 1, 1), (1, 1, -1)}.

1, 1, 3, 9, 34, 120, 478, 1872, 7709, 31816, 134780, 573835, 2480705, 10788275, 47350778, 209012171, 928390519, 4143344634, 18578397587, 83628064271, 377823717954, 1712465596226, 7784693924479, 35483172148019, 162133273349314, 742501767345115, 3407417532270014, 15666937100794566

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + 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: A149001 A149002 A204446 * A149004 A149005 A149006

Adjacent sequences: A149000 A149001 A149002 * A149004 A149005 A149006

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved