A149005 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, 1), (0, 1, 1), (1, -1, 1), (1, 0, -1)}.

1, 1, 3, 9, 34, 120, 480, 1864, 7724, 31399, 133843, 559593, 2429122, 10390671, 45665183, 198653628, 881804068, 3883630079, 17376449963, 77271811239, 347946089164, 1559298429090, 7059064851180, 31835156778887, 144779224351473, 656409486987982, 2996888762486011, 13649315320686171

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A204446 A149003 A149004 * A149006 A149007 A053791

Adjacent sequences: A149002 A149003 A149004 * A149006 A149007 A149008

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved