A150183 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), (0, 0, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 6, 20, 80, 294, 1168, 4700, 19616, 80936, 341652, 1451138, 6240682, 26900956, 116808978, 509503870, 2235781132, 9846065742, 43506965704, 192855619628, 857932000186, 3827546695256, 17114951919858, 76699514623644, 344535118116958, 1551000876073158, 6994631039368602, 31595691327084332

Offset

0,2

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A027221 A346747 A300514 * A150184 A150185 A354737

Adjacent sequences: A150180 A150181 A150182 * A150184 A150185 A150186

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved